-
Previous Article
On the singular-hyperbolicity of star flows
- JMD Home
- This Issue
-
Next Article
Growth rate of periodic orbits for geodesic flows over surfaces with radially symmetric focusing caps
Limit theorems for skew translations
1. | School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom |
References:
[1] |
A. Bufetov, Limit theorems for translation flows, Ann. of Math. (2), 179 (2014), 431-499.
doi: 10.4007/annals.2014.179.2.2. |
[2] |
A. Bufetov and G. Forni, Limit theorems for horocycle flows,, , ().
|
[3] |
A. Bufetov and B. Solomyak, Limit theorems for self-similar tilings, Comm. Math. Phys., 319 (2013), 761-789.
doi: 10.1007/s00220-012-1624-7. |
[4] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations I. Convex bodies, Geom. Funct. Anal., 24 (2014), 85-115.
doi: 10.1007/s00039-014-0254-y. |
[5] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations II. Boxes,, , ().
|
[6] |
F. Cellarosi, Limiting curlicue measures for theta sums, Ann. Inst. Henri Poincaré Probab. Stat., 47 (2011), 466-497.
doi: 10.1214/10-AIHP361. |
[7] |
A. Fedotov and F. Klopp, An exact renormalization formula for Gaussian exponential sums and applications, Amer. J. Math., 134 (2012), 711-748.
doi: 10.1353/ajm.2012.0016. |
[8] |
L. Flaminio and G. Forni, Equidistribution of nilflows and applications to theta sums, Ergodic Theory Dynam. Systems, 26 (2006), 409-433.
doi: 10.1017/S014338570500060X. |
[9] |
W. B. Jurkat and J. W. Van Horne, The proof of the central limit theorem for theta sums, Duke Math. J., 48 (1981), 873-885.
doi: 10.1215/S0012-7094-81-04848-1. |
[10] |
W. B. Jurkat and J. W. Van Horne, On the central limit theorem for theta series, Michigan Math. J., 29 (1982), 65-77.
doi: 10.1307/mmj/1029002615. |
[11] |
W. B. Jurkat and J. W. Van Horne, The uniform central limit theorem for theta sums, Duke Math. J., 50 (1983), 649-666.
doi: 10.1215/S0012-7094-83-05030-5. |
[12] |
H. Kesten, Uniform distribution mod 1, Ann. of Math. (2), 71 (1960), 445-471.
doi: 10.2307/1969938. |
[13] |
H. Kesten, Uniform distribution mod 1. II,, Acta Arith., 7 (): 355.
|
[14] |
J. Marklof, Limit theorems for theta sums, Duke Math. J., 97 (1999), 127-153.
doi: 10.1215/S0012-7094-99-09706-5. |
[15] |
J. Marklof, Almost modular functions and the distribution of $n^2 x$ modulo one, Int. Math. Res. Not., 39 (2003), 2131-2151.
doi: 10.1155/S1073792803130292. |
[16] |
J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. (2), 158 (2003), 419-471.
doi: 10.4007/annals.2003.158.419. |
[17] |
Y. G. Sinai and C. Ulcigrai, A limit theorem for Birkhoff sums of nonintegrable functions over rotations, in Geometric and Probabilistic Structures in Dynamics, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008, 317-340.
doi: 10.1090/conm/469/09174. |
show all references
References:
[1] |
A. Bufetov, Limit theorems for translation flows, Ann. of Math. (2), 179 (2014), 431-499.
doi: 10.4007/annals.2014.179.2.2. |
[2] |
A. Bufetov and G. Forni, Limit theorems for horocycle flows,, , ().
|
[3] |
A. Bufetov and B. Solomyak, Limit theorems for self-similar tilings, Comm. Math. Phys., 319 (2013), 761-789.
doi: 10.1007/s00220-012-1624-7. |
[4] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations I. Convex bodies, Geom. Funct. Anal., 24 (2014), 85-115.
doi: 10.1007/s00039-014-0254-y. |
[5] |
D. Dolgopyat and B. Fayad, Deviations of ergodic sums for toral translations II. Boxes,, , ().
|
[6] |
F. Cellarosi, Limiting curlicue measures for theta sums, Ann. Inst. Henri Poincaré Probab. Stat., 47 (2011), 466-497.
doi: 10.1214/10-AIHP361. |
[7] |
A. Fedotov and F. Klopp, An exact renormalization formula for Gaussian exponential sums and applications, Amer. J. Math., 134 (2012), 711-748.
doi: 10.1353/ajm.2012.0016. |
[8] |
L. Flaminio and G. Forni, Equidistribution of nilflows and applications to theta sums, Ergodic Theory Dynam. Systems, 26 (2006), 409-433.
doi: 10.1017/S014338570500060X. |
[9] |
W. B. Jurkat and J. W. Van Horne, The proof of the central limit theorem for theta sums, Duke Math. J., 48 (1981), 873-885.
doi: 10.1215/S0012-7094-81-04848-1. |
[10] |
W. B. Jurkat and J. W. Van Horne, On the central limit theorem for theta series, Michigan Math. J., 29 (1982), 65-77.
doi: 10.1307/mmj/1029002615. |
[11] |
W. B. Jurkat and J. W. Van Horne, The uniform central limit theorem for theta sums, Duke Math. J., 50 (1983), 649-666.
doi: 10.1215/S0012-7094-83-05030-5. |
[12] |
H. Kesten, Uniform distribution mod 1, Ann. of Math. (2), 71 (1960), 445-471.
doi: 10.2307/1969938. |
[13] |
H. Kesten, Uniform distribution mod 1. II,, Acta Arith., 7 (): 355.
|
[14] |
J. Marklof, Limit theorems for theta sums, Duke Math. J., 97 (1999), 127-153.
doi: 10.1215/S0012-7094-99-09706-5. |
[15] |
J. Marklof, Almost modular functions and the distribution of $n^2 x$ modulo one, Int. Math. Res. Not., 39 (2003), 2131-2151.
doi: 10.1155/S1073792803130292. |
[16] |
J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. (2), 158 (2003), 419-471.
doi: 10.4007/annals.2003.158.419. |
[17] |
Y. G. Sinai and C. Ulcigrai, A limit theorem for Birkhoff sums of nonintegrable functions over rotations, in Geometric and Probabilistic Structures in Dynamics, Contemp. Math., 469, Amer. Math. Soc., Providence, RI, 2008, 317-340.
doi: 10.1090/conm/469/09174. |
[1] |
Jean-Pierre Conze, Stéphane Le Borgne, Mikaël Roger. Central limit theorem for stationary products of toral automorphisms. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1597-1626. doi: 10.3934/dcds.2012.32.1597 |
[2] |
James Nolen. A central limit theorem for pulled fronts in a random medium. Networks and Heterogeneous Media, 2011, 6 (2) : 167-194. doi: 10.3934/nhm.2011.6.167 |
[3] |
Oliver Díaz-Espinosa, Rafael de la Llave. Renormalization and central limit theorem for critical dynamical systems with weak external noise. Journal of Modern Dynamics, 2007, 1 (3) : 477-543. doi: 10.3934/jmd.2007.1.477 |
[4] |
Shige Peng. Law of large numbers and central limit theorem under nonlinear expectations. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 4-. doi: 10.1186/s41546-019-0038-2 |
[5] |
Yves Derriennic. Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the "central limit theorem''. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 143-158. doi: 10.3934/dcds.2006.15.143 |
[6] |
Michael Björklund, Alexander Gorodnik. Central limit theorems in the geometry of numbers. Electronic Research Announcements, 2017, 24: 110-122. doi: 10.3934/era.2017.24.012 |
[7] |
Mathias Staudigl. A limit theorem for Markov decision processes. Journal of Dynamics and Games, 2014, 1 (4) : 639-659. doi: 10.3934/jdg.2014.1.639 |
[8] |
Kariane Calta, John Smillie. Algebraically periodic translation surfaces. Journal of Modern Dynamics, 2008, 2 (2) : 209-248. doi: 10.3934/jmd.2008.2.209 |
[9] |
José A. Conejero, Alfredo Peris. Chaotic translation semigroups. Conference Publications, 2007, 2007 (Special) : 269-276. doi: 10.3934/proc.2007.2007.269 |
[10] |
Martin Swaczyna, Petr Volný. Uniform motions in central fields. Journal of Geometric Mechanics, 2017, 9 (1) : 91-130. doi: 10.3934/jgm.2017004 |
[11] |
Sergey Kryzhevich, Sergey Tikhomirov. Partial hyperbolicity and central shadowing. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2901-2909. doi: 10.3934/dcds.2013.33.2901 |
[12] |
Benjamin Dozier. Equidistribution of saddle connections on translation surfaces. Journal of Modern Dynamics, 2019, 14: 87-120. doi: 10.3934/jmd.2019004 |
[13] |
Armengol Gasull, Francesc Mañosas. Subseries and signed series. Communications on Pure and Applied Analysis, 2019, 18 (1) : 479-492. doi: 10.3934/cpaa.2019024 |
[14] |
Roy Adler, Bruce Kitchens, Michael Shub. Stably ergodic skew products. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 349-350. doi: 10.3934/dcds.1996.2.349 |
[15] |
Pascal Hubert, Gabriela Schmithüsen. Infinite translation surfaces with infinitely generated Veech groups. Journal of Modern Dynamics, 2010, 4 (4) : 715-732. doi: 10.3934/jmd.2010.4.715 |
[16] |
Wolf-Jürgen Beyn, Raphael Kruse. Two-sided error estimates for the stochastic theta method. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 389-407. doi: 10.3934/dcdsb.2010.14.389 |
[17] |
Meenakshi Rana, Shruti Sharma. Combinatorics of some fifth and sixth order mock theta functions. Electronic Research Archive, 2021, 29 (1) : 1803-1818. doi: 10.3934/era.2020092 |
[18] |
Shengxin Zhu. Summation of Gaussian shifts as Jacobi's third Theta function. Mathematical Foundations of Computing, 2020, 3 (3) : 157-163. doi: 10.3934/mfc.2020015 |
[19] |
Weidong Zhao, Jinlei Wang, Shige Peng. Error estimates of the $\theta$-scheme for backward stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 905-924. doi: 10.3934/dcdsb.2009.12.905 |
[20] |
Bram van Asch, Frans Martens. Lee weight enumerators of self-dual codes and theta functions. Advances in Mathematics of Communications, 2008, 2 (4) : 393-402. doi: 10.3934/amc.2008.2.393 |
2020 Impact Factor: 0.848
Tools
Metrics
Other articles
by authors
[Back to Top]