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Topological entropy for set-valued maps
A note on specification for iterated function systems
| 1. | Department of Mathematics, Universidade Federal do Rio de Janeiro, Rio de Janeiro-RJ, CT, 21945-970, Brazil |
| 2. | Mathematics Department, The Pennsylvania State University, State College, PA 16802, United States |
| 3. | Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810 |
References:
| [1] |
R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414.
doi: 10.1090/S0002-9947-1971-0274707-X. |
| [2] |
M. Denker, Y. Kifer and M. Stadlbauer, Thermodynamic formalism for random countable Markov shifts, Discrete Contin. Dyn. Syst., 22 (2008), 131-164.
doi: 10.3934/dcds.2008.22.131. |
| [3] |
M. Denker, Einführung in die Analysis Dynamischer Systeme, Springer-Lehrbuch, Springer-Verlag, Berlin, 2005. |
| [4] |
M. Denker and M. Yuri, Conformal families of measures for general iterated function systems, Contemporary Math., 631 (2015), 93-108.
doi: 10.1090/conm/631/12598. |
| [5] |
B. M. Gurevic, Topological entropy for denumerable Markov chains, Dokl. Akad. Nauk., SSSR 187 (1969), 715-718; Engl. transl. in Soviet Math. Dokl., 10 (1969), 911-915. |
| [6] |
O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergodic Theory & Dynamical Systems, 19 (1999), 1565-1593.
doi: 10.1017/S0143385799146820. |
| [7] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
show all references
References:
| [1] |
R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc., 153 (1971), 401-414.
doi: 10.1090/S0002-9947-1971-0274707-X. |
| [2] |
M. Denker, Y. Kifer and M. Stadlbauer, Thermodynamic formalism for random countable Markov shifts, Discrete Contin. Dyn. Syst., 22 (2008), 131-164.
doi: 10.3934/dcds.2008.22.131. |
| [3] |
M. Denker, Einführung in die Analysis Dynamischer Systeme, Springer-Lehrbuch, Springer-Verlag, Berlin, 2005. |
| [4] |
M. Denker and M. Yuri, Conformal families of measures for general iterated function systems, Contemporary Math., 631 (2015), 93-108.
doi: 10.1090/conm/631/12598. |
| [5] |
B. M. Gurevic, Topological entropy for denumerable Markov chains, Dokl. Akad. Nauk., SSSR 187 (1969), 715-718; Engl. transl. in Soviet Math. Dokl., 10 (1969), 911-915. |
| [6] |
O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergodic Theory & Dynamical Systems, 19 (1999), 1565-1593.
doi: 10.1017/S0143385799146820. |
| [7] |
P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982. |
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