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On large deviations for amenable group actions
1. | School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210023, China, China |
2. | School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, Jiangsu |
References:
[1] |
R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136.
doi: 10.1090/S0002-9947-1973-0338317-X. |
[2] |
M. Brin and A. Katok, On local entropy, Lecture Notes in Mathematics, Springer, Berlin, 1007 (1983), 30-38.
doi: 10.1007/BFb0061408. |
[3] |
N. Chung, Topological pressure and the variational principle for actions of sofic groups, Ergod. Th. Dynam. Sys., 33 (2013), 1363-1390.
doi: 10.1017/S0143385712000429. |
[4] |
N. Chung and H. Li, Homoclinic group, IE group, and expansive algebraic actions, Invent. Math., 199 (2015), 805-858.
doi: 10.1007/s00222-014-0524-1. |
[5] |
T. Downarowicz, D. Huczek and G. Zhang, Tilings of amenable groups, to appear in J. Reine Angew. Math., arXiv:1502.02413v1. |
[6] |
A. Eizenberg, Y. Kifer and B. Weiss, Large deviations for $Z^d$-Actions, Comm. Math. Physics, 164 (1994), 433-454.
doi: 10.1007/BF02101485. |
[7] |
R. S. Ellis, Entropy, Large Deviations and Statistical Mechanics, Springer-Verlag, New York, 1985.
doi: 10.1007/978-1-4613-8533-2. |
[8] |
W. Huang, X. Ye and G. Zhang, Local entropy theory for a countable discrete amenable group action, J. Funct. Anal., 261 (2011), 1028-1082.
doi: 10.1016/j.jfa.2011.04.014. |
[9] |
A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math. I.H.E.S., 51 (1980), 137-173. |
[10] |
Y. Kifer, Multidimensional random subshifts of finite type and their large deviations, Probability Theory and Related Fields, 103 (1995), 223-248.
doi: 10.1007/BF01204216. |
[11] |
E. Lindenstrauss, Pointwise theorems for amenable groups, Invent. Math., 146 (2001), 259-295.
doi: 10.1007/s002220100162. |
[12] |
B. Liang and K. Yan, Topological pressure for sub-additive potentials of amenable group actions, J. Funct. Anal., 262 (2012), 584-601.
doi: 10.1016/j.jfa.2011.09.020. |
[13] |
J. M. Ollagnier, Ergodic Theory and Statistical Mechanics, Lecture Notes in Math. 1115, Springer-Verlag, Berlin, 1985.
doi: 10.1007/BFb0101575. |
[14] |
J. M. Ollagnier and D. Pinchon, The variational principle, Studia Math., 72 (1982), 151-159. |
[15] |
D. S. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math., 48 (1987), 1-141.
doi: 10.1007/BF02790325. |
[16] |
L. Rey-Bellet and L.-S. Young, Large deviations in non-uniformly hyperbolic dynamical systems, Ergod. Th. Dynam. Sys., 28 (2008), 587-612.
doi: 10.1017/S0143385707000478. |
[17] |
A. Shulman, Maximal ergodic theorems on groups, Dep. Lit. NIINTI, No.2184, 1988. |
[18] |
A. M. Stepin and A. T. Tagi-Zade, Variational characterization of topological pressure of the amenable groups of transformations, Dokl. Akad. Nauk SSSR, 254 (1980), 545-549 (in Russian). |
[19] |
T. Ward and Q. Zhang, The Abramov-Rokhlin entropy addition formula for amenable group action, Monatshefte für Mathematik, 114 (1992), 317-329.
doi: 10.1007/BF01299386. |
[20] |
B. Weiss, Actions of amenable groups, in Topics in Dynamics and Ergodic Theory, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 310 (2003), 226-262.
doi: 10.1017/CBO9780511546716.012. |
[21] |
L.-S. Young, Some large deviation results for dynamical systems, Trans. Amer. Math. Soc., 318 (1990), 525-543.
doi: 10.2307/2001318. |
[22] |
D. Zheng and E. Chen, Bowen entropy for actions of amenable groups, Israel J. Math., 212 (2016), 895-911.
doi: 10.1007/s11856-016-1312-y. |
show all references
References:
[1] |
R. Bowen, Topological entropy for noncompact sets, Trans. Amer. Math. Soc., 184 (1973), 125-136.
doi: 10.1090/S0002-9947-1973-0338317-X. |
[2] |
M. Brin and A. Katok, On local entropy, Lecture Notes in Mathematics, Springer, Berlin, 1007 (1983), 30-38.
doi: 10.1007/BFb0061408. |
[3] |
N. Chung, Topological pressure and the variational principle for actions of sofic groups, Ergod. Th. Dynam. Sys., 33 (2013), 1363-1390.
doi: 10.1017/S0143385712000429. |
[4] |
N. Chung and H. Li, Homoclinic group, IE group, and expansive algebraic actions, Invent. Math., 199 (2015), 805-858.
doi: 10.1007/s00222-014-0524-1. |
[5] |
T. Downarowicz, D. Huczek and G. Zhang, Tilings of amenable groups, to appear in J. Reine Angew. Math., arXiv:1502.02413v1. |
[6] |
A. Eizenberg, Y. Kifer and B. Weiss, Large deviations for $Z^d$-Actions, Comm. Math. Physics, 164 (1994), 433-454.
doi: 10.1007/BF02101485. |
[7] |
R. S. Ellis, Entropy, Large Deviations and Statistical Mechanics, Springer-Verlag, New York, 1985.
doi: 10.1007/978-1-4613-8533-2. |
[8] |
W. Huang, X. Ye and G. Zhang, Local entropy theory for a countable discrete amenable group action, J. Funct. Anal., 261 (2011), 1028-1082.
doi: 10.1016/j.jfa.2011.04.014. |
[9] |
A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math. I.H.E.S., 51 (1980), 137-173. |
[10] |
Y. Kifer, Multidimensional random subshifts of finite type and their large deviations, Probability Theory and Related Fields, 103 (1995), 223-248.
doi: 10.1007/BF01204216. |
[11] |
E. Lindenstrauss, Pointwise theorems for amenable groups, Invent. Math., 146 (2001), 259-295.
doi: 10.1007/s002220100162. |
[12] |
B. Liang and K. Yan, Topological pressure for sub-additive potentials of amenable group actions, J. Funct. Anal., 262 (2012), 584-601.
doi: 10.1016/j.jfa.2011.09.020. |
[13] |
J. M. Ollagnier, Ergodic Theory and Statistical Mechanics, Lecture Notes in Math. 1115, Springer-Verlag, Berlin, 1985.
doi: 10.1007/BFb0101575. |
[14] |
J. M. Ollagnier and D. Pinchon, The variational principle, Studia Math., 72 (1982), 151-159. |
[15] |
D. S. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math., 48 (1987), 1-141.
doi: 10.1007/BF02790325. |
[16] |
L. Rey-Bellet and L.-S. Young, Large deviations in non-uniformly hyperbolic dynamical systems, Ergod. Th. Dynam. Sys., 28 (2008), 587-612.
doi: 10.1017/S0143385707000478. |
[17] |
A. Shulman, Maximal ergodic theorems on groups, Dep. Lit. NIINTI, No.2184, 1988. |
[18] |
A. M. Stepin and A. T. Tagi-Zade, Variational characterization of topological pressure of the amenable groups of transformations, Dokl. Akad. Nauk SSSR, 254 (1980), 545-549 (in Russian). |
[19] |
T. Ward and Q. Zhang, The Abramov-Rokhlin entropy addition formula for amenable group action, Monatshefte für Mathematik, 114 (1992), 317-329.
doi: 10.1007/BF01299386. |
[20] |
B. Weiss, Actions of amenable groups, in Topics in Dynamics and Ergodic Theory, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 310 (2003), 226-262.
doi: 10.1017/CBO9780511546716.012. |
[21] |
L.-S. Young, Some large deviation results for dynamical systems, Trans. Amer. Math. Soc., 318 (1990), 525-543.
doi: 10.2307/2001318. |
[22] |
D. Zheng and E. Chen, Bowen entropy for actions of amenable groups, Israel J. Math., 212 (2016), 895-911.
doi: 10.1007/s11856-016-1312-y. |
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