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December  2015, 20(10): 3475-3485. doi: 10.3934/dcdsb.2015.20.3475

A note on specification for iterated function systems

Welington Cordeiro 1, , Manfred Denker 2, and  Michiko Yuri 3,

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

Received  December 2014 Revised  March 2015 Published  September 2015

We introduce several notions of specification for iterated function systems and exhibit some of their dynamical properties. In particular, we show that topological entropy and algebraic pressure [4] of systems with specification are approximable by the corresponding expressions for finitely generated iterated function systems.
Keywords: Iterated function system, specification, entropy, pressure, mixing..
Mathematics Subject Classification: 28D20, 28D99, 37A25, 37A30, 37B40, 37C30, 37D3.
Citation: Welington Cordeiro, Manfred Denker, Michiko Yuri. A note on specification for iterated function systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3475-3485. doi: 10.3934/dcdsb.2015.20.3475
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.  Google Scholar

[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.  Google Scholar

[3]

M. Denker, Einführung in die Analysis Dynamischer Systeme, Springer-Lehrbuch, Springer-Verlag, Berlin, 2005.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[6]

O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergodic Theory & Dynamical Systems, 19 (1999), 1565-1593. doi: 10.1017/S0143385799146820.  Google Scholar

[7]

P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[3]

M. Denker, Einführung in die Analysis Dynamischer Systeme, Springer-Lehrbuch, Springer-Verlag, Berlin, 2005.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[6]

O. Sarig, Thermodynamic formalism for countable Markov shifts, Ergodic Theory & Dynamical Systems, 19 (1999), 1565-1593. doi: 10.1017/S0143385799146820.  Google Scholar

[7]

P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, 79, Springer-Verlag, New York-Berlin, 1982.  Google Scholar

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