Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A note on specification for iterated function systems

Pages: 3475 - 3485, Volume 20, Issue 10, December 2015      doi:10.3934/dcdsb.2015.20.3475

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Welington Cordeiro - Department of Mathematics, Universidade Federal do Rio de Janeiro, Rio de Janeiro-RJ, CT, 21945-970, Brazil (email)
Manfred Denker - Mathematics Department, The Pennsylvania State University, State College, PA 16802, United States (email)
Michiko Yuri - Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan (email)

Abstract: 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, entropy, pressure, specification, mixing.
Mathematics Subject Classification:  28D20, 28D99, 37A25, 37A30, 37B40, 37C30, 37D35.

Received: December 2014;      Revised: March 2015;      Available Online: September 2015.