|
[1]
|
J. Aaronson and H. Nakada, Trimmed sums for non-negative, mixing stationary processes, Stochastic Process. Appl., 104 (2003), 173-192.
doi: 10.1016/S0304-4149(02)00236-3.
|
|
[2]
|
M. Abadi, Poisson approximations via Chen-Stein for non-Markov processes, Progr. Probab., 60 (2008), 1-19.
doi: 10.1007/978-3-7643-8786-0_1.
|
|
[3]
|
M. Abadi and N. Vergne, Sharp errors for point-wise Poisson approximations in mixing processes, Nonlinearity, 21 (2008), 2871-2885.
doi: 10.1088/0951-7715/21/12/008.
|
|
[4]
|
R. Aimino, M. Nicol and M. Todd, Recurrence statistics for the space of interval exchange maps and the Teichmuller flow on the space of translation surfaces, Ann. Inst. Henri Poincaré Probab. Stat., 53 (2017), 1371-1401.
doi: 10.1214/16-AIHP758.
|
|
[5]
|
D. Aldous, Probability approximations via the Poisson clumping heuristic, Applied Math. Sci., 77 (1989), 269 pp.
doi: 10.1007/978-1-4757-6283-9.
|
|
[6]
|
D. V. Anosov and Y. G. Sinai, Certain smooth ergodic systems, Russian Math. Surveys, 22 (1967), 103-167.
|
|
[7]
|
J. S. Athreya, Logarithm laws and shrinking target properties, Proc. Indian Acad. Sci. Math. Sci., 119 (2009), 541-557.
doi: 10.1007/s12044-009-0044-x.
|
|
[8]
|
J. S. Athreya, Random affine lattices, Contemp. Math., 639 (2015), 169-174.
doi: 10.1090/conm/639/12793.
|
|
[9]
|
J. S. Athreya, A. Ghosh and J. Tseng, Spiraling of approximations and spherical averages of Siegel transforms, J. Lond. Math. Soc., 91 (2015), 383-404.
doi: 10.1112/jlms/jdu082.
|
|
[10]
|
J. S. Athreya and G. A. Margulis, Logarithm laws for unipotent flows-Ⅰ, J. Mod. Dyn., 3 (2009), 359-378.
doi: 10.3934/jmd.2009.3.359.
|
|
[11]
|
J. S. Athreya and G. A. Margulis, Logarithm laws for unipotent flows-Ⅱ, J. Mod. Dyn., 11 (2017), 1-16.
doi: 10.3934/jmd.2017001.
|
|
[12]
|
J. S. Athreya, A. Parrish and J. Tseng, Ergodic theory and Diophantine approximation for translation surfaces and linear forms, Nonlinearity, 29 (2016), 2173-2190.
doi: 10.1088/0951-7715/29/8/2173.
|
|
[13]
|
M. Babillot and M. Peigne, Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps, Bull. Soc. Math. France, 134 (2006), 119-163.
doi: 10.24033/bsmf.2503.
|
|
[14]
|
D. Badziahin, V. Beresnevich and S. Velani, Inhomogeneous theory of dual Diophantine approximation on manifolds, Adv. Math., 232 (2013), 1-35.
doi: 10.1016/j.aim.2012.09.022.
|
|
[15]
|
L. Barreira, Y. Pesin and J. Schmeling, Dimension and product structure of hyperbolic measures, Ann. of Math., 149 (1999), 755-783.
doi: 10.2307/121072.
|
|
[16]
|
L. Barreira and B. Saussol, Hausdorff dimension of measures via Poincaré recurrence, Comm. Math. Phys., 219 (2001), 443-463.
doi: 10.1007/s002200100427.
|
|
[17]
|
M. B. Bekka and M. Mayer, Ergodic theory and topological dynamics of group actions on homogeneous spaces, London Math. Soc. Lecture Note Ser., 269 (2000), 200 pp.
doi: 10.1017/CBO9780511758898.
|
|
[18]
|
R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry, Springer, Berlin, 1992.
doi: 10.1007/978-3-642-58158-8.
|
|
[19]
|
V. I. Bernik and M. M. Dodson, Metric Diophantine approximation on manifolds, Cambridge Tracts in Mathematics, 137 (1999), 172 pp.
doi: 10.1017/CBO9780511565991.
|
|
[20]
|
M. Björklund, M. Einsiedler and A. Gorodnik, Quantitative multiple mixing, JEMS, 22 (2020), 1475-1529.
doi: 10.4171/JEMS/949.
|
|
[21]
|
M. Björklund and A. Gorodnik, Central limit theorems in the geometry of numbers, Electron. Res. Announc. Math. Sci., 24 (2017), 110-122.
doi: 10.3934/era.2017.24.012.
|
|
[22]
|
M. Björklund and A. Gorodnik, Central limit theorems for group actions which are exponentially mixing of all orders, Journal d'Analyse Mathematiques, 141 (2020), 457-482.
doi: 10.1007/s11854-020-0106-7.
|
|
[23]
|
M. Björklund and A. Gorodnik, Central limit theorems for Diophantine approximants, Math. Ann., 374 (2019), 1371-1437.
doi: 10.1007/s00208-019-01828-1.
|
|
[24]
|
R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms. 2d revised ed., Springer Lecture Notes in Math, 470 (2008), 75 pp.
|
|
[25]
|
H. Bruin and M. Todd, Return time statistics of invariant measures for interval maps with positive Lyapunov exponent, Stoch. Dyn., 9 (2009), 81-100.
doi: 10.1142/S0219493709002567.
|
|
[26]
|
H. Bruin and S. Vaienti, Return time statistics for unimodal maps, Fund. Math., 176 (2003), 77-94.
doi: 10.4064/fm176-1-6.
|
|
[27]
|
M. Carney, M. Holland and M. Nicol, Extremes and extremal indices for level set observables on hyperbolic systems, Nonlinearity, 34 (2021), 1136-1167.
doi: 10.1088/1361-6544/abd85f.
|
|
[28]
|
M. Carney and M. Nicol, Dynamical Borel–Cantelli lemmas and rates of growth of Birkhoff sums of non-integrable observables on chaotic dynamical systems, Nonlinearity, 30 (2017), 2854-2870.
doi: 10.1088/1361-6544/aa72c2.
|
|
[29]
|
M. Carvalho, A. C. M. Freitas, J. M. Freitas, M. Holland and M. Nicol, Extremal dichotomy for uniformly hyperbolic systems, Dyn. Syst., 30 (2015), 383-403.
doi: 10.1080/14689367.2015.1056722.
|
|
[30]
|
A. Castro, Fast mixing for attractors with a mostly contracting central direction, Ergodic Theory Dynam. Systems, 24 (2004), 17-44.
doi: 10.1017/S0143385703000294.
|
|
[31]
|
J. Chaika, Shrinking targets for IETs: Extending a theorem of Kurzweil, GAFA, 21 (2011), 1020-1042.
doi: 10.1007/s00039-011-0130-y.
|
|
[32]
|
J. Chaika and D. Constantine, Quantitative shrinking target properties for rotations and interval exchanges, Israel J. Math., 230 (2019), 275-334.
doi: 10.1007/s11856-018-1824-8.
|
|
[33]
|
J.-R. Chazottes and P. Collet, Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems, Ergodic Theory Dynam. Sys., 33 (2013), 49-80.
doi: 10.1017/S0143385711000897.
|
|
[34]
|
J.-R. Chazottes and E. Ugalde, Entropy estimation and fluctuations of hitting and recurrence times for Gibbsian sources, Discrete Contin. Dyn. Syst. B, 5 (2005), 565-586.
doi: 10.3934/dcdsb.2005.5.565.
|
|
[35]
|
N. I. Chernov, Limit theorems and Markov approximations for chaotic dynamical systems, Probab. Theory Related Fields, 101 (1995), 321-362.
doi: 10.1007/BF01200500.
|
|
[36]
|
N. Chernov, Entropy, Lyapunov exponents, and mean free path for billiards, J. Statist. Phys., 88 (1997), 1-29.
doi: 10.1007/BF02508462.
|
|
[37]
|
N. Chernov and D. Kleinbock, Dynamical Borel–Cantelli lemmas for Gibbs measures, Israel J. Math., 122 (2001), 1-27.
doi: 10.1007/BF02809888.
|
|
[38]
|
G. H. Choe and B. K. Seo, Recurrence speed of multiples of an irrational number, Proc. Japan Acad. Ser. A Math. Sci., 77 (2001), 134-137.
|
|
[39]
|
Z. Coelho, Asymptotic laws for symbolic dynamical processes, London Math. Soc. Lecture Notes, 279 (2000), 123-165.
|
|
[40]
|
P. Collet, Statistics of closest return for some non-uniformly hyperbolic systems, Ergodic Theory Dynam. Systems, 21 (2001), 401-420.
doi: 10.1017/S0143385701001201.
|
|
[41]
|
P. Collet, A. Galves and B. Schmitt, Repetition times for Gibbsian sources, Nonlinearity, 12 (1999), 1225-1237.
doi: 10.1088/0951-7715/12/4/326.
|
|
[42]
|
I. P. Cornfeld, S. V. Fomin and Y. G. Sinai, Ergodic Theory, Grundlehren der Mathematischen Wissenschaften, 245, Springer, New York, 1982.
doi: 10.1007/978-1-4615-6927-5.
|
|
[43]
|
S. G. Dani, Divergent trajectories of flows on homogeneous spaces and Diophantine approximation, J. Reine Angew. Math., 359 (1985), 55-89.
doi: 10.1515/crll.1985.359.55.
|
|
[44]
|
M. Denker and N. Kan, Om Sevastyanov's theorem, Stat. Probab. Lett., 77 (2007), 272-279.
doi: 10.1016/j.spl.2006.07.008.
|
|
[45]
|
H. G. Diamond and J. D. Vaaler, Estimates for partial sums of continued fraction partial quotients, Pacific J. Math., 122 (1986), 73-82.
doi: 10.2140/pjm.1986.122.73.
|
|
[46]
|
W. Doeblin, Remarques sur la théorie métrique des fractions continues, Compositio Math., 7 (1940), 353-371.
|
|
[47]
|
D. Dolgopyat, On dynamics of mostly contracting diffeomorphisms, Comm. Math. Phys., 213 (2000), 181-201.
doi: 10.1007/s002200000238.
|
|
[48]
|
D. Dolgopyat, Limit theorems for partially hyperbolic systems, Trans. Amer. Math. Soc., 356 (2004), 1637-1689.
doi: 10.1090/S0002-9947-03-03335-X.
|
|
[49]
|
D. Dolgopyat, C. Dong, A. Kanigowski and P. Nandori, Mixing properties of generalized $T, T^{-1}$ transformations, Israel J. Math., 247 (2022), no. 1, 21–73.
doi: 10.1007/s11856-022-2289-3.
|
|
[50]
|
D. Dolgopyat and B. Fayad, Limit theorems for toral translations, Hyperbolic dynamics, fluctuations and large deviations, 89 (2015), 227-277.
doi: 10.1090/pspum/089/01492.
|
|
[51]
|
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations Ⅱ: Squares, Publ. IHES, 132 (2020), 293-352.
doi: 10.1007/s10240-020-00120-2.
|
|
[52]
|
D. Dolgopyat, B. Fayad and I. Vinogradov, Central limit theorems for simultaneous Diophantine approximations, J. Éc. Polytech. Math., 4 (2017), 1-35.
doi: 10.5802/jep.37.
|
|
[53]
|
D. Dolgopyat, A. Kanigowski and F. R. Hertz, Exponential mixing implies Bernoulli, arXiv: 2106.03147.
|
|
[54]
|
D. Dolgopyat and O. Sarig, Quenched and annealed temporal limit theorems for circle rotations, Asterisque, 415 (2020), 57-83.
doi: 10.24033/ast.
|
|
[55]
|
L. E. Dubins and D. A. Freedman, A sharper form of the Borel–Cantelli lemma and the strong law, Ann. Math. Statist., 36 (1965), 800-807.
doi: 10.1214/aoms/1177700054.
|
|
[56]
|
N. Enriquez and Y. L. Jan, Statistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature, Rev. Mat. Iberoamericana, 13 (1997), 377-401.
doi: 10.4171/RMI/225.
|
|
[57]
|
M. L. Einsiedler, D. A. Ellwood, A. Eskin, D. Kleinbock, E. Lindenstrauss, G. Margulis, S. Marmi and J.-C. Yoccoz (editors): Homogeneous Flows, Moduli Spaces and Arithmetic, Clay Mathematics Proceedings, 10, 2010.
|
|
[58]
|
D. El-Baz, J. Marklof and I. Vinogradov, The distribution of directions in an affine lattice: Two-point correlations and mixed moments, IMRN, 2015 (2015), 1371-1400.
doi: 10.1093/imrn/rnt258.
|
|
[59]
|
A. Eskin, Counting problems and semisimple groups, Doc. Math., II (1998), 539-552.
|
|
[60]
|
B. Fayad, Mixing in the absence of the shrinking target property, Bull. London Math. Soc., 38 (2006), 829-838.
doi: 10.1112/S0024609306018546.
|
|
[61]
|
J. L. Fernandez, M. V. Melian and D. Pestana, Expanding maps, shrinking targets and hitting times, Nonlinearity, 25 (2012), 2443-2471.
doi: 10.1088/0951-7715/25/9/2443.
|
|
[62]
|
D. Freedman, Another note on the Borel–Cantelli Lemma and the strong law with the Poisson approximation as a by-product, Ann. Probability, 1 (1973), 910-925.
doi: 10.1214/aop/1176996800.
|
|
[63]
|
A. C. M. Freitas, J. M. Freitas and M. Magalhães, Convergence of marked point processes of excesses for dynamical systems, J. Eur. Math. Soc., 20 (2018), 2131-2179.
doi: 10.4171/JEMS/808.
|
|
[64]
|
A. C. M. Freitas, J. M. Freitas and M. Magalhães, Complete convergence and records for dynamically generated stochastic processes, Trans. Amer. Math. Soc., 373 (2020), 435-478.
doi: 10.1090/tran/7922.
|
|
[65]
|
A. C. M. Freitas, J. M. Freitas, F. Rodrigues and J. V. Soares, Rare events for Cantor target sets, Comm. Math. Phys., 378 (2020), 75-115.
doi: 10.1007/s00220-020-03794-1.
|
|
[66]
|
A. C. M. Freitas, J. M. Freitas and M. Todd, Hitting time statistics and extreme value theory, Probab. Theory Related Fields, 147 (2010), 675-710.
doi: 10.1007/s00440-009-0221-y.
|
|
[67]
|
S. Galatolo, Dimension via waiting time and recurrence, Math. Res. Lett., 12 (2005), 377-386.
doi: 10.4310/MRL.2005.v12.n3.a8.
|
|
[68]
|
S. Galatolo, Dimension and hitting in rapidly mixing system, Math. Res. Lett., 14 (2007), 797-805.
doi: 10.4310/MRL.2007.v14.n5.a8.
|
|
[69]
|
S. Galatolo, Hitting time in regular sets and logarithm law for rapidly mixing dynamical systems, Proc. Amer. Math. Soc., 138 (2010), 2477-2487.
doi: 10.1090/S0002-9939-10-10275-5.
|
|
[70]
|
S. Galatolo and I. Nisoli, Shrinking targets in fast mixing flows and the geodesic flow on negatively curved manifolds, Nonlinearity, 24 (2011), 3099-3113.
doi: 10.1088/0951-7715/24/11/005.
|
|
[71]
|
S. Galatolo and P. Peterlongo, Long hitting time, slow decay of correlations and arithmetical properties, Discrete Contin. Dyn. Syst., 27 (2010), 185-204.
doi: 10.3934/dcds.2010.27.185.
|
|
[72]
|
A. Ghosh and D. Kelmer, Shrinking targets for semisimple groups, Bull. Lond. Math. Soc., 49 (2017), 235-245.
doi: 10.1112/blms.12023.
|
|
[73]
|
A. Gorodnik and A. Nevo, Quantitative ergodic theorems and their number-theoretic applications, Bull. Lond. Math. Soc., 52 (2015), 65-113.
doi: 10.1090/S0273-0979-2014-01462-4.
|
|
[74]
|
A. Gorodnik and R. Spatzier, Exponential mixing of nilmanifold automorphisms, J. Anal. Math., 123 (2014), 355-396.
doi: 10.1007/s11854-014-0024-7.
|
|
[75]
|
S. Gouëzel, A Borel–Cantelli lemma for intermittent interval maps, Nonlinearity, 20 (2007), 1491-1497.
doi: 10.1088/0951-7715/20/6/010.
|
|
[76]
|
A. Groshev, A theorem on a system of linear forms, Dokl. Akad. Nauk SSSR, 19 (1938), 151-152.
|
|
[77]
|
Y. Guivarch and Y. L. Jan, Asymptotic winding of the geodesic flow on modular surfaces and continued fractions, Ann. Sci. École Norm. Sup., 26 (1993), 23–50; 29 (1996), 811–814.
doi: 10.24033/asens.1755.
|
|
[78]
|
C. Gupta, M. Nicol and W. Ott, A Borel–Cantelli lemma for nonuniformly expanding dynamical systems, Nonlinearity, 23 (2010), 1991-2008.
doi: 10.1088/0951-7715/23/8/010.
|
|
[79]
|
N. Haydn, The central limit theorem for uniformly strong mixing measures, Stoch. Dyn., 12 (2012), 1250006, 31 pp.
doi: 10.1142/S0219493712500062.
|
|
[80]
|
N. Haydn, Entry and return times distribution, Dyn. Syst., 28 (2013), 333-353.
doi: 10.1080/14689367.2013.822459.
|
|
[81]
|
N. Haydn and S. Vaienti, Limiting entry and return times distribution for arbitrary null sets, Comm. Math. Phys., 378 (2020), 149-184.
doi: 10.1007/s00220-020-03795-0.
|
|
[82]
|
N. Haydn, M. Nicol, T. Persson and S. Vaienti, A note on Borel–Cantelli lemmas for non-uniformly hyperbolic dynamical systems, Ergodic Theory Dynam. Systems, 33 (2013), 475-498.
doi: 10.1017/S014338571100099X.
|
|
[83]
|
N. Haydn, M. Nicol, S. Vaienti and L. Zhang, Central limit theorems for the shrinking target problem, J. Stat. Phys, 153 (2013), 864-887.
doi: 10.1007/s10955-013-0860-3.
|
|
[84]
|
N. T. A. Haydn and Y. Psiloyenis, Return times distribution for Markov towers with decay of correlations, Nonlinearity, 27 (2014), 1323-1349.
doi: 10.1088/0951-7715/27/6/1323.
|
|
[85]
|
N. Haydn and S. Vaienti, The limiting distribution and error terms for return times of dynamical systems, Discrete Contin. Dyn. Syst., 10 (2004), 589-616.
doi: 10.3934/dcds.2004.10.589.
|
|
[86]
|
N. Haydn and S. Vaienti, Fluctuations of the metric entropy for mixing measures, Stoch. Dyn., 4 (2004), 595-627.
doi: 10.1142/S021949370400119X.
|
|
[87]
|
N. Haydn and S. Vaienti, Limiting entry times distribution for arbitrary null sets, Comm. Math. Phys., 378 (2020), 149-184.
doi: 10.1007/s00220-020-03795-0.
|
|
[88]
|
N. T. A. Haydn and K. Wasilewska, Limiting distribution and error terms for the number of visits to balls in nonuniformly hyperbolic dynamical systems, Discrete Contin. Dyn. Syst., 36 (2016), 2585-2611.
doi: 10.3934/dcds.2016.36.2585.
|
|
[89]
|
R. Hill and S. Velani, The ergodic theory of shrinking targets, Invent. Math., 119 (1995), 175-198.
doi: 10.1007/BF01245179.
|
|
[90]
|
M. Hirata, Poisson law for Axiom A diffeomorphisms, Ergodic Theory Dynam. Systems, 13 (1993), 533-556.
doi: 10.1017/S0143385700007513.
|
|
[91]
|
M. Hirata, Poisson law for the dynamical systems with self-mixing conditions, in Dynamical Systems and Chaos, Vol. 1 (Hachioji, 1994), World Sci. Publ., River Edge, NJ, 1995, 87–96.
|
|
[92]
|
M. Hirata, B. Saussol and S. Vaienti, Statistics of return times: A general framework and new applications, Comm. Math. Phys., 206 (1999), 33-55.
doi: 10.1007/s002200050697.
|
|
[93]
|
F. Hofbauer and G. Keller, Ergodic properties of invariant measures for piecewise monotonic transformations, in The Theory of Chaotic Attractors, B. R. Hunt, T. Y. Li, J. A. Kennedy, H. E. Nusse (eds), Springer, New York, 1982.
doi: 10.1007/BF01215004.
|
|
[94]
|
M. Holland, M. Kirsebom, P. Kunde and T. Persson, Dichotomy results for eventually always hitting time statistics and almost sure growth of extremes, arXiv: 2109.06314.
|
|
[95]
|
I. A. Ibragimov, Some limit theorems for stationary processes, (Russian), Teor. Verojatnost. i Primenen., 7 (1962), 361-392.
|
|
[96]
|
J. Jaerisch, M. Kessebohmer and B. O. Stratmann, A Fréchet law and an Erdös–Philipp law for maximal cuspidal windings, Ergodic Theory Dynam. Systems, 33 (2013), 1008-1028.
doi: 10.1017/S0143385712000235.
|
|
[97]
|
G. Keller, Rare events, exponential hitting times and extremal indices via spectral perturbation, Dyn. Syst., 27 (2012), 11-27.
doi: 10.1080/14689367.2011.653329.
|
|
[98]
|
D. Kelmer, Shrinking targets for discrete time flows on hyperbolic manifolds, Geom. Funct. Anal., 27 (2017), 1257-1287.
doi: 10.1007/s00039-017-0421-z.
|
|
[99]
|
D. Kelmer and H. Oh, Exponential mixing and shrinking targets for geodesic flow on geometrically finite hyperbolic manifolds, J. Mod. Dyn., 17 (2021), 401-434.
doi: 10.3934/jmd.2021014.
|
|
[100]
|
D. Kelmer and S. Yu, Shrinking target problems for flows on homogeneous spaces, Trans. Amer. Math. Soc., 372 (2019), 6283-6314.
doi: 10.1090/tran/7783.
|
|
[101]
|
M. Kesseböhmer and T. Schindler, Strong laws of large numbers for intermediately trimmed Birkhoff sums of observables with infinite mean, Stoch. Process. Appl., 129 (2019), 4163-4207.
doi: 10.1016/j.spa.2018.11.015.
|
|
[102]
|
H. Kesten and R. A. Maller, Ratios of trimmed sums and order statistics, Ann. Probab., 20 (1992), 1805-1842.
|
|
[103]
|
A. Y. Khintchine, Einige Sätze über Kettenbruche, mit Anwendungen auf die Theorie der Diophantischen Approximationen, (German) Math. Ann., 92 (1924), 115–125.
doi: 10.1007/BF01448437.
|
|
[104]
|
A. Y. Khintchine, Continued Fractions, Dover, Mineola, NY, 1997.
|
|
[105]
|
M. Kirsebom, P. Kunde and T. Persson, Shrinking targets and eventually always hitting points for interval maps, Nonlinearity, 33 (2020), no. 2, 892–914.
doi: 10.1088/1361-6544/ab5160.
|
|
[106]
|
D. H. Kim, The shrinking target property of irrational rotations, Nonlinearity, 20 (2007), 1637-1643.
doi: 10.1088/0951-7715/20/7/006.
|
|
[107]
|
D. H. Kim, The dynamical Borel–Cantelli lemma for interval maps, Discrete Contin. Dyn. Syst., 17 (2007), 891-900.
doi: 10.3934/dcds.2007.17.891.
|
|
[108]
|
D. H. Kim, Refined shrinking target property of rotations, Nonlinearity, 27 (2014), 1985-1997.
doi: 10.1088/0951-7715/27/9/1985.
|
|
[109]
|
D. H. Kim and B. K. Seo, The waiting time for irrational rotations, Nonlinearity, 16 (2003), 1861-1868.
doi: 10.1088/0951-7715/16/5/318.
|
|
[110]
|
D. Kleinbock, Some applications of homogeneous dynamics to number theory, Smooth ergodic theory and its applications (Seattle, WA, 1999), 69 (2001), 639-660.
doi: 10.1090/pspum/069/1858548.
|
|
[111]
|
D. Kleinbock, I. Konstantoulas and F. K. Richter, Zero-one laws for eventually always hitting points in mixing systems, arXiv: 1904.08584.
|
|
[112]
|
D. Y. Kleinbock and G. A. Margulis, Bounded orbits of nonquasiunipotent flows on homogeneous spaces, Amer. Math. Soc. Transl. Ser. 2, 171 (1996), 141-172.
doi: 10.1090/trans2/171/11.
|
|
[113]
|
D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds, Ann. Math., 148 (1998), 339-360.
doi: 10.2307/120997.
|
|
[114]
|
D. Y. Kleinbock and G. A. Margulis, Logarithm laws for flows on homogeneous spaces, Invent. Math., 138 (1999), 451-494.
doi: 10.1007/s002220050350.
|
|
[115]
|
D. Y. Kleinbock and G. A. Margulis, On effective equidistribution of expanding translates of certain orbits in the space of lattices, Number Theory, Analysis and Geometry, Springer, New York, 2012, 385–396.
doi: 10.1007/978-1-4614-1260-1_18.
|
|
[116]
|
D. Kleinbock, N. Shah and A. Starkov, Dynamics of subgroup actions on homogeneous spaces of Lie groups and applications to number theory, Handbook of Dynamical Systems, Vol. 1A (2002), North-Holland, Amsterdam, 813–930.
doi: 10.1016/S1874-575X(02)80013-3.
|
|
[117]
|
D. Kleinbock, R. Shi and B. Weiss, Pointwise equidistribution with an error rate and with respect to unbounded functions, Math. Ann., 36 (2017), 857-879.
doi: 10.1007/s00208-016-1404-3.
|
|
[118]
|
D. Y. Kleinbock and X. Zhao, An application of lattice points counting to shrinking target problems, Discrete Contin. Dyn. Syst., 38 (2018), 155-168.
doi: 10.3934/dcds.2018007.
|
|
[119]
|
G. Knieper, Hyperbolic dynamics and Riemannian geometry, Handbook of Dynamical Systems, Vol. 1A, 453, North-Holland, Amsterdam, 2002.
doi: 10.1016/S1874-575X(02)80008-X.
|
|
[120]
|
J. Kurzweil, On the metric theory of inhomogeneous Diophantine approximations, Studia Math., 15 (1955), 84-112.
doi: 10.4064/sm-15-1-84-112.
|
|
[121]
|
M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer, New York–Berlin, 1983.
|
|
[122]
|
F. Ledrappier and L.-S. Young, The metric entropy of diffeomorphisms. Part Ⅱ. Relations between entropy, exponents and dimension, Ann. Math., 122 (1985), 540-574.
doi: 10.2307/1971329.
|
|
[123]
|
R. Leplaideur and B. Saussol, Central limit theorem for dimension of Gibbs measures in hyperbolic dynamics, Stoch. Dyn., 12 (2012), 1150019, 24 pp.
doi: 10.1142/S0219493712003675.
|
|
[124]
|
C. Liverani, On contact Anosov flows, Ann. of Math. (2), 159 (2004), 1275-1312.
doi: 10.4007/annals.2004.159.1275.
|
|
[125]
|
V. Lucarini, D. Faranda, A. de Freitas, J. de Freitas, M. Holland, T. Kuna, M. Nicol, M. Todd and S. Vaienti, Extremes and Recurrence in Dynamical Systems, John Wiley, Hoboken, NJ, 2016.
doi: 10.1002/9781118632321.
|
|
[126]
|
J. Marklof, The $n$-point correlations between values of a linear form, Ergodic Theory Dynam. Systems, 20 (2000), 1127-1172.
doi: 10.1017/S0143385700000626.
|
|
[127]
|
J. Marklof, Distribution modulo one and Ratner's theorem, Equidistribution in Number Theory, an Introduction, 237 (2007), 217-244.
doi: 10.1007/978-1-4020-5404-4_11.
|
|
[128]
|
J. Marklof, Entry and return times for semi-flows, Nonlinearity, 30 (2017), 810-824.
doi: 10.1088/1361-6544/aa518b.
|
|
[129]
|
F. Maucourant, Dynamical Borel–Cantelli lemma for hyperbolic spaces, Israel J. Math., 152 (2006), 143-155.
doi: 10.1007/BF02771980.
|
|
[130]
|
T. Mori, The strong law of large numbers when extreme terms are excluded from sums, Z. Wahrsch. Verw. Gebiete, 36 (1976), 189-194.
doi: 10.1007/BF00532544.
|
|
[131]
|
F. Paccaut, Statistics of return times for weighted maps of the interval, Ann. Inst. H. Poincare Probab. Statist., 36 (2000), 339-366.
doi: 10.1016/S0246-0203(00)00127-8.
|
|
[132]
|
M. J. Pacifico and F. Yang, Hitting times distribution and extreme value laws for semi-flows, Discrete Contin. Dyn. Syst., 37 (2017), 5861-5881.
doi: 10.3934/dcds.2017255.
|
|
[133]
|
W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque, 187-188 (1990), 268 pp.
|
|
[134]
|
F. Paulin and M. Pollicott, Logarithm laws for equilibrium states in negative curvature, Comm. Math. Phys., 346 (2016), 1-34.
doi: 10.1007/s00220-016-2652-5.
|
|
[135]
|
F. Pène and B. Saussol, Back to balls in billiards, Comm. Math. Phys., 293 (2010), 837-866.
doi: 10.1007/s00220-009-0911-4.
|
|
[136]
|
F. Pène and B. Saussol, Poisson law for some non-uniformly hyperbolic dynamical systems with polynomial rate of mixing, Ergodic Theory Dynam. Systems, 36 (2016), 2602-2626.
doi: 10.1017/etds.2015.28.
|
|
[137]
|
W. Philipp, Some metric theorems in number theory, Pacific J. Math, 20 (1967), 109-127.
doi: 10.2140/pjm.1967.20.109.
|
|
[138]
|
B. Pitskel, Poisson limit law for Markov chains, Ergodic Theory Dynam. Sys., 11 (1991), 501-513.
doi: 10.1017/S0143385700006301.
|
|
[139]
|
S. Ross, A First Course in Probability, 8th edition, Macmillan Co., New York; Collier Macmillan Ltd., London, 2010.
|
|
[140]
|
J. Rousseau, Recurrence rates for observations of flows, Ergodic Theory Dynam. Systems, 32 (2012), 1727-1751.
doi: 10.1017/S014338571100037X.
|
|
[141]
|
J. Rousseau, Hitting time statistics for observations of dynamical systems, Nonlinearity, 27 (2014), 2377-2392.
doi: 10.1088/0951-7715/27/9/2377.
|
|
[142]
|
B. Saussol, On fluctuations and the exponential statistics of return times, Nonlinearity, 14 (2001), 179-191.
doi: 10.1088/0951-7715/14/1/311.
|
|
[143]
|
B. Saussol, Recurrence rate in rapidly mixing dynamical systems, Discrete Contin. Dyn. Syst., 15 (2006), 259-267.
doi: 10.3934/dcds.2006.15.259.
|
|
[144]
|
B. Saussol, An introduction to quantitative Poincaré recurrence in dynamical systems, Rev. Math. Phys., 21 (2009), 949-979.
doi: 10.1142/S0129055X09003785.
|
|
[145]
|
C. Series, The modular surface and continued fractions, J. London Math. Soc., 31 (1985), 69-80.
doi: 10.1112/jlms/s2-31.1.69.
|
|
[146]
|
B. A. A. Sevastjanov, Possion limit law in a scheme of sums of dependent random variables, (Russian) Teor. Verojatnost. i Primenen., 17 (1972), 733–738.
|
|
[147]
|
D. Simmons, An analogue of a theorem of Kurzweil, Nonlinearity, 28 (2015), 1401-1408.
doi: 10.1088/0951-7715/28/5/1401.
|
|
[148]
|
Y. G. Sinai, Gibbs measures in ergodic theory, Russian Math. Surveys, 27 (1972), 21-69.
|
|
[149]
|
V. G. Sprindžuk, Metric theory of Diophantine approximations, V. H. Winston & Sons, Washington, D.C. (1979).
|
|
[150]
|
M. A. Stenlund, Strong pair correlation bound implies the CLT for Sinai billiards, J. Stat. Phys., 140 (2010), 154-169.
doi: 10.1007/s10955-010-9987-7.
|
|
[151]
|
B. Stratmann and S. L. Velani, The Patterson measure for geometrically finite groups with parabolic elements, new and old, Proc. London Math. Soc. (3), 71 (1995), 197-220.
doi: 10.1112/plms/s3-71.1.197.
|
|
[152]
|
D. Sullivan, Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics, Acta Math., 149 (1982), 215-237.
doi: 10.1007/BF02392354.
|
|
[153]
|
J. Tseng, On circle rotations and the shrinking target properties, Discrete Contin. Dyn. Syst., 20 (2008), 1111-1122.
doi: 10.3934/dcds.2008.20.1111.
|
|
[154]
|
P. Varandas, Correlation decay and recurrence asymptotics for some robust nonuniformly hyperbolic maps, J. Stat. Phys., 133 (2008), 813-839.
doi: 10.1007/s10955-008-9639-3.
|
|
[155]
|
M. Viana, Stochastic Dynamics of Deterministic Systems, Rio de Janeiro: IMPA, 1997.
|
|
[156]
|
I. Vinogradov, Limiting distribution of visits of several rotations to shrinking intervals, preprint.
|
|
[157]
|
D. Williams, Probability with Martingales, Cambridge Math. Textbooks. Cambridge University Press, Cambridge, 1991.
doi: 10.1017/CBO9780511813658.
|
|
[158]
|
F. Yang, Rare event process and entry times distribution for arbitrary null sets on compact manifolds, Ann. Inst. Henri Poincare Probab. Stat., 57 (2021), 1103-1135.
doi: 10.1214/20-aihp1109.
|
|
[159]
|
L.-S. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. Math., 147 (1998), 585-650.
doi: 10.2307/120960.
|
|
[160]
|
X. Zhang, Note on limit distribution of normalized return times and escape rate, Stoch. Dyn., 16 (2016), 1660014, 15 pp.
doi: 10.1142/S0219493716600145.
|
{{journal.titleEn}} 
Download:
