Topological pressure for an iterated function system

Abstract

In this paper, we introduce a notion of topological pressure, which is different from the LMW's and ML's for an iterated function system. We find out the properties of the topological pressure, which are more similar to the properties of the classical topological pressure than LMW's and ML's. For an iterated function system, we obtain a partial variational principle on topological pressure, which improves the LMW's related result. Finally, we give a lower bound estimation of the topological pressure for a Ruelle-expanding iterated function system. In particular, we point out the exponential growth rate of fixed points is a lower bound of WLLZ's topological entropy for a Ruelle-expanding iterated function system.

Keywords:

• Topological entropy
• topological pressure
• iterated function system
• measure-theoretic entropy

2010 Mathematics Subject Classifications:

• Primary: 37C50
• Secondary: 37C15

Acknowledgments

The authors thank the referee for the careful reading and many valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This article is supported by the National Nature Science Funds of China [grant number 11771149].