Topological pressure for an iterated function system. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Wang, Huoyun; Liao, Xing
• Is Part Of: Dynamical systems. Volume 36:Issue 3(2021)
• Page Start: 483
• Page End: 506
• Publication Date: 2021-07-03
• Subjects: Topological entropy -- topological pressure -- iterated function system -- measure-theoretic entropy; Primary: 37C50 -- Secondary: 37C15; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2021.1929081
• Languages: English
• ISSNs: 1468-9367

Abstract

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.