-
Previous Article
The entropy of Lyapunov-optimizing measures of some matrix cocycles
- JMD Home
- This Volume
-
Next Article
Minimality of the Ehrenfest wind-tree model
Effective equidistribution of translates of maximal horospherical measures in the space of lattices
1. | Department of Mathematics, University of Texas, 1 University Station, Austin, TX 78712, United States |
2. | Department of Mathematics, University of Michigan, 530 Church St., Ann Arbor, MI 48109, United States |
3. | Department of Mathematics and Computer Science, Wesleyan University, 265 Church Street, Middletown, CT 06459, United States |
References:
[1] |
V. Bernik, D. Kleinbock and G. A. Margulis, Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions,, Internat. Math. Res. Notices, (2001), 453.
doi: 10.1155/S1073792801000241. |
[2] |
A. Borel and J. Tits, Groupes réductifs,, Inst. Hautes Études Sci. Publ. Math., 27 (1965), 55.
|
[3] |
S. G. Dani, Invariant measures of horospherical flows on noncompact homogeneous spaces,, Invent. Math., 47 (1978), 101.
doi: 10.1007/BF01578067. |
[4] |
W. Duke, Z. Rudnick and P. Sarnak, Density of integer points on affine homogeneous varieties,, Duke Math. J., 71 (1993), 143.
doi: 10.1215/S0012-7094-93-07107-4. |
[5] |
A. Eskin and C. McMullen, Mixing, counting, and equidistribution in Lie groups,, Duke Math. J., 71 (1993), 181.
doi: 10.1215/S0012-7094-93-07108-6. |
[6] |
J. Franke, Y. I. Manin and Y. Tschinkel, Rational points of bounded height on Fano varieties,, Invent. Math., 95 (1989), 421.
doi: 10.1007/BF01393904. |
[7] |
J. E. Humphreys, Linear Algebraic Groups,, Graduate Texts in Mathematics, (1975).
|
[8] |
D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds,, Ann. of Math. (2), 148 (1998), 339.
doi: 10.2307/120997. |
[9] |
D. Y. Kleinbock and G. A. Margulis, On effective equidistribution of expanding translates of certain orbits in the space of lattices,, in Number Theory, (2012), 385.
doi: 10.1007/978-1-4614-1260-1_18. |
[10] |
D. Kleinbock, R. Shi and B. Weiss, Pointwise equidistribution with an error rate and with respect to unbounded functions,, , (2015). Google Scholar |
[11] |
D. Kleinbock and B. Weiss, Dirichlet's theorem on Diophantine approximation and homogeneous flows,, J. Mod. Dyn., 2 (2008), 43.
|
[12] |
G. A. Margulis, On some aspects of the theory of Anosov systems,, Springer Monographs in Mathematics, (2004).
doi: 10.1007/978-3-662-09070-1. |
[13] |
A. Mohammadi and A. S. Golsefidy, Translate of horospheres and counting problems,, Amer. J. Math., 136 (2014), 1301.
doi: 10.1353/ajm.2014.0037. |
[14] |
H. Oh, Orbital counting via mixing and unipotent flows,, in Homogeneous Flows, (2010), 339.
|
[15] |
P. Sarnak, Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series,, Comm. Pure Appl. Math., 34 (1981), 719.
doi: 10.1002/cpa.3160340602. |
[16] |
A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series,, J. Indian Math. Soc. (N.S.), 20 (1956), 47.
|
[17] |
N. Shah and B. Weiss, On actions of epimorphic subgroups on homogeneous spaces,, Ergodic Theory Dynam. Systems, 20 (2000), 567.
doi: 10.1017/S0143385700000298. |
[18] |
N. A. Shah, Limit distributions of expanding translates of certain orbits on homogeneous spaces,, Proc. Indian Acad. Sci. Math. Sci., 106 (1996), 105.
doi: 10.1007/BF02837164. |
[19] |
R. Shi, Expanding cone and applications to homogeneous dynamics,, , (2015). Google Scholar |
[20] |
D. Zagier, Eisenstein series and the Riemann zeta-function,, in Automorphic Forms, (1981), 275.
|
show all references
References:
[1] |
V. Bernik, D. Kleinbock and G. A. Margulis, Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions,, Internat. Math. Res. Notices, (2001), 453.
doi: 10.1155/S1073792801000241. |
[2] |
A. Borel and J. Tits, Groupes réductifs,, Inst. Hautes Études Sci. Publ. Math., 27 (1965), 55.
|
[3] |
S. G. Dani, Invariant measures of horospherical flows on noncompact homogeneous spaces,, Invent. Math., 47 (1978), 101.
doi: 10.1007/BF01578067. |
[4] |
W. Duke, Z. Rudnick and P. Sarnak, Density of integer points on affine homogeneous varieties,, Duke Math. J., 71 (1993), 143.
doi: 10.1215/S0012-7094-93-07107-4. |
[5] |
A. Eskin and C. McMullen, Mixing, counting, and equidistribution in Lie groups,, Duke Math. J., 71 (1993), 181.
doi: 10.1215/S0012-7094-93-07108-6. |
[6] |
J. Franke, Y. I. Manin and Y. Tschinkel, Rational points of bounded height on Fano varieties,, Invent. Math., 95 (1989), 421.
doi: 10.1007/BF01393904. |
[7] |
J. E. Humphreys, Linear Algebraic Groups,, Graduate Texts in Mathematics, (1975).
|
[8] |
D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds,, Ann. of Math. (2), 148 (1998), 339.
doi: 10.2307/120997. |
[9] |
D. Y. Kleinbock and G. A. Margulis, On effective equidistribution of expanding translates of certain orbits in the space of lattices,, in Number Theory, (2012), 385.
doi: 10.1007/978-1-4614-1260-1_18. |
[10] |
D. Kleinbock, R. Shi and B. Weiss, Pointwise equidistribution with an error rate and with respect to unbounded functions,, , (2015). Google Scholar |
[11] |
D. Kleinbock and B. Weiss, Dirichlet's theorem on Diophantine approximation and homogeneous flows,, J. Mod. Dyn., 2 (2008), 43.
|
[12] |
G. A. Margulis, On some aspects of the theory of Anosov systems,, Springer Monographs in Mathematics, (2004).
doi: 10.1007/978-3-662-09070-1. |
[13] |
A. Mohammadi and A. S. Golsefidy, Translate of horospheres and counting problems,, Amer. J. Math., 136 (2014), 1301.
doi: 10.1353/ajm.2014.0037. |
[14] |
H. Oh, Orbital counting via mixing and unipotent flows,, in Homogeneous Flows, (2010), 339.
|
[15] |
P. Sarnak, Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series,, Comm. Pure Appl. Math., 34 (1981), 719.
doi: 10.1002/cpa.3160340602. |
[16] |
A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series,, J. Indian Math. Soc. (N.S.), 20 (1956), 47.
|
[17] |
N. Shah and B. Weiss, On actions of epimorphic subgroups on homogeneous spaces,, Ergodic Theory Dynam. Systems, 20 (2000), 567.
doi: 10.1017/S0143385700000298. |
[18] |
N. A. Shah, Limit distributions of expanding translates of certain orbits on homogeneous spaces,, Proc. Indian Acad. Sci. Math. Sci., 106 (1996), 105.
doi: 10.1007/BF02837164. |
[19] |
R. Shi, Expanding cone and applications to homogeneous dynamics,, , (2015). Google Scholar |
[20] |
D. Zagier, Eisenstein series and the Riemann zeta-function,, in Automorphic Forms, (1981), 275.
|
[1] |
Thomas Frenzel, Matthias Liero. Effective diffusion in thin structures via generalized gradient systems and EDP-convergence. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 395-425. doi: 10.3934/dcdss.2020345 |
[2] |
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020272 |
[3] |
Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020349 |
[4] |
Giuseppina Guatteri, Federica Masiero. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020048 |
[5] |
Fanni M. Sélley. A self-consistent dynamical system with multiple absolutely continuous invariant measures. Journal of Computational Dynamics, 2021, 8 (1) : 9-32. doi: 10.3934/jcd.2021002 |
[6] |
Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100 |
[7] |
George W. Patrick. The geometry of convergence in numerical analysis. Journal of Computational Dynamics, 2021, 8 (1) : 33-58. doi: 10.3934/jcd.2021003 |
[8] |
Matania Ben–Artzi, Joseph Falcovitz, Jiequan Li. The convergence of the GRP scheme. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 1-27. doi: 10.3934/dcds.2009.23.1 |
[9] |
Gui-Qiang Chen, Beixiang Fang. Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 85-114. doi: 10.3934/dcds.2009.23.85 |
[10] |
Azmy S. Ackleh, Nicolas Saintier. Diffusive limit to a selection-mutation equation with small mutation formulated on the space of measures. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1469-1497. doi: 10.3934/dcdsb.2020169 |
[11] |
Thierry Horsin, Mohamed Ali Jendoubi. On the convergence to equilibria of a sequence defined by an implicit scheme. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020465 |
[12] |
Philipp Harms. Strong convergence rates for markovian representations of fractional processes. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020367 |
[13] |
Alberto Bressan, Carlotta Donadello. On the convergence of viscous approximations after shock interactions. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 29-48. doi: 10.3934/dcds.2009.23.29 |
[14] |
Parikshit Upadhyaya, Elias Jarlebring, Emanuel H. Rubensson. A density matrix approach to the convergence of the self-consistent field iteration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 99-115. doi: 10.3934/naco.2020018 |
[15] |
Gang Luo, Qingzhi Yang. The point-wise convergence of shifted symmetric higher order power method. Journal of Industrial & Management Optimization, 2021, 17 (1) : 357-368. doi: 10.3934/jimo.2019115 |
[16] |
Toshiko Ogiwara, Danielle Hilhorst, Hiroshi Matano. Convergence and structure theorems for order-preserving dynamical systems with mass conservation. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3883-3907. doi: 10.3934/dcds.2020129 |
[17] |
Xiuli Xu, Xueke Pu. Optimal convergence rates of the magnetohydrodynamic model for quantum plasmas with potential force. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 987-1010. doi: 10.3934/dcdsb.2020150 |
[18] |
Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388 |
[19] |
Matúš Tibenský, Angela Handlovičová. Convergence analysis of the discrete duality finite volume scheme for the regularised Heston model. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1181-1195. doi: 10.3934/dcdss.2020226 |
[20] |
Wei Ouyang, Li Li. Hölder strong metric subregularity and its applications to convergence analysis of inexact Newton methods. Journal of Industrial & Management Optimization, 2021, 17 (1) : 169-184. doi: 10.3934/jimo.2019105 |
2019 Impact Factor: 0.465
Tools
Metrics
Other articles
by authors
[Back to Top]