Saturatedness of dynamical systems under the almost specification property. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Mesón, Alejandro; Vericat, Fernando
• Is Part Of: Journal of dynamical systems and geometric theories. Volume 14:Issue 1(2016)
• Page Start: 1
• Page End: 15
• Publication Date: 2016-01-02
• Subjects: 37C45 -- 37B40; Almost specification property -- V—statistics; Differentiable dynamical systems -- Periodicals; Geometry -- Periodicals; Differentiable dynamical systems; Geometry; Periodicals; 515.39
• DOI: 10.1080/1726037X.2016.1177917
• Languages: English
• ISSNs: 1726-037X

Abstract

Abstract: A dynamical system is saturated when for any invariant measure μ, the topological entropy of the set of the μ —generic points equals the measure-theoretic entropy of the system. This fact was confirmed by Fan, Liao and Peyrière for systems with specification. In a recent article we extended this result under the condition of non-uniform specification. In this work we consider another weaker condition than specification called almost specification property. This concept was introduced by Thompson as a modification of the almost property product by Pfister and Sullivan. We prove herein the saturatedness of systems under the Thompson condition. The saturatedness is a key point to establish a variational principle for V —statistics, as was developed by Fan, Schmeling and Wu.