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Brief survey on the topological entropy
Entropy and actions of sofic groups
1. | Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904 |
References:
[1] |
R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy,, Trans. Amer. Math. Soc., 114 (1965), 309.
doi: 10.1090/S0002-9947-1965-0175106-9. |
[2] |
L. Bowen, A measure-conjugacy invariant for free group actions,, Annals of Math., 171 (2010), 1387.
doi: 10.4007/annals.2010.171.1387. |
[3] |
L. Bowen, Measure conjugacy invariants for actions of countable sofic groups,, J. Amer. Math. Soc., 23 (2010), 217.
doi: 10.1090/S0894-0347-09-00637-7. |
[4] |
L. Bowen, Weak isomorphisms between Bernoulli shifts,, Israel J. Math., 183 (2011), 93.
doi: 10.1007/s11856-011-0043-3. |
[5] |
M. Gromov, Endomorphisms of symbolic algebraic varieties,, J. Eur. Math. Soc., 1 (1999), 109.
doi: 10.1007/PL00011162. |
[6] |
M. Gromov, Topological invariants of dynamical systems and spaces of holomorphic maps. I,, Math. Phys. Anal. Geom., 2 (1999), 323.
doi: 10.1023/A:1009841100168. |
[7] |
M. Keane and M. Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic,, Ann. of Math., 109 (1979), 397.
doi: 10.2307/1971117. |
[8] |
D. Kerr, Sofic measure entropy via finite partitions,, Groups Geom. Dyn., 7 (2013), 617.
doi: 10.4171/GGD/200. |
[9] |
D. Kerr, Bernoulli actions of sofic groups have completely positive entropy,, Israel J. Math., 202 (2014), 461.
doi: 10.1007/s11856-014-1077-0. |
[10] |
D. Kerr and H. Li, Entropy and the variational principle for actions of sofic groups,, Invent. Math., 186 (2011), 501.
doi: 10.1007/s00222-011-0324-9. |
[11] |
H. Li, Sofic mean dimension,, Adv. Math., 244 (2013), 570.
doi: 10.1016/j.aim.2013.05.005. |
[12] |
E. Lindenstrauss, Mean dimension, small entropy factors and an embedding theorem,, Inst. Hautes Études Sci. Publ. Math., 89 (1999), 227.
|
[13] |
E. Lindenstrauss and B. Weiss, Mean topological dimension,, Israel J. Math., 115 (2000), 1.
doi: 10.1007/BF02810577. |
[14] |
D. Ornstein, Newton's laws and coin tossing,, Notices Amer. Math. Soc., 60 (2013), 450.
doi: 10.1090/noti974. |
[15] |
D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups,, J. Analyse Math., 48 (1987), 1.
doi: 10.1007/BF02790325. |
[16] |
V. A. Rohlin, Generators in ergodic theory,, Vest. Leningrad Univ., 18 (1963), 26.
|
[17] |
V. Rohlin and Y. Sinai, The structure and properties of invariant measurable partitions,, Dokl. Akad. Nauk SSSR, 141 (1961), 1038.
|
[18] |
D. Rudolph and B. Weiss, Entropy and mixing for amenable group actions,, Ann. of Math., 151 (2000), 1119.
doi: 10.2307/121130. |
[19] |
A. Stepin, Bernoulli shifts on groups,, Dokl. Akad. Nauk SSSR, 223 (1975), 300.
|
[20] |
J.-P. Thouvenot, Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l'un est un schéma de Bernoulli,, Israel J. Math., 21 (1975), 177.
doi: 10.1007/BF02760797. |
[21] |
B. Weiss, Sofic groups and dynamical systems,, Sankhya Series A, 62 (2000), 350.
|
show all references
References:
[1] |
R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy,, Trans. Amer. Math. Soc., 114 (1965), 309.
doi: 10.1090/S0002-9947-1965-0175106-9. |
[2] |
L. Bowen, A measure-conjugacy invariant for free group actions,, Annals of Math., 171 (2010), 1387.
doi: 10.4007/annals.2010.171.1387. |
[3] |
L. Bowen, Measure conjugacy invariants for actions of countable sofic groups,, J. Amer. Math. Soc., 23 (2010), 217.
doi: 10.1090/S0894-0347-09-00637-7. |
[4] |
L. Bowen, Weak isomorphisms between Bernoulli shifts,, Israel J. Math., 183 (2011), 93.
doi: 10.1007/s11856-011-0043-3. |
[5] |
M. Gromov, Endomorphisms of symbolic algebraic varieties,, J. Eur. Math. Soc., 1 (1999), 109.
doi: 10.1007/PL00011162. |
[6] |
M. Gromov, Topological invariants of dynamical systems and spaces of holomorphic maps. I,, Math. Phys. Anal. Geom., 2 (1999), 323.
doi: 10.1023/A:1009841100168. |
[7] |
M. Keane and M. Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic,, Ann. of Math., 109 (1979), 397.
doi: 10.2307/1971117. |
[8] |
D. Kerr, Sofic measure entropy via finite partitions,, Groups Geom. Dyn., 7 (2013), 617.
doi: 10.4171/GGD/200. |
[9] |
D. Kerr, Bernoulli actions of sofic groups have completely positive entropy,, Israel J. Math., 202 (2014), 461.
doi: 10.1007/s11856-014-1077-0. |
[10] |
D. Kerr and H. Li, Entropy and the variational principle for actions of sofic groups,, Invent. Math., 186 (2011), 501.
doi: 10.1007/s00222-011-0324-9. |
[11] |
H. Li, Sofic mean dimension,, Adv. Math., 244 (2013), 570.
doi: 10.1016/j.aim.2013.05.005. |
[12] |
E. Lindenstrauss, Mean dimension, small entropy factors and an embedding theorem,, Inst. Hautes Études Sci. Publ. Math., 89 (1999), 227.
|
[13] |
E. Lindenstrauss and B. Weiss, Mean topological dimension,, Israel J. Math., 115 (2000), 1.
doi: 10.1007/BF02810577. |
[14] |
D. Ornstein, Newton's laws and coin tossing,, Notices Amer. Math. Soc., 60 (2013), 450.
doi: 10.1090/noti974. |
[15] |
D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups,, J. Analyse Math., 48 (1987), 1.
doi: 10.1007/BF02790325. |
[16] |
V. A. Rohlin, Generators in ergodic theory,, Vest. Leningrad Univ., 18 (1963), 26.
|
[17] |
V. Rohlin and Y. Sinai, The structure and properties of invariant measurable partitions,, Dokl. Akad. Nauk SSSR, 141 (1961), 1038.
|
[18] |
D. Rudolph and B. Weiss, Entropy and mixing for amenable group actions,, Ann. of Math., 151 (2000), 1119.
doi: 10.2307/121130. |
[19] |
A. Stepin, Bernoulli shifts on groups,, Dokl. Akad. Nauk SSSR, 223 (1975), 300.
|
[20] |
J.-P. Thouvenot, Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l'un est un schéma de Bernoulli,, Israel J. Math., 21 (1975), 177.
doi: 10.1007/BF02760797. |
[21] |
B. Weiss, Sofic groups and dynamical systems,, Sankhya Series A, 62 (2000), 350.
|
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