High pointwise emergence and Katok's conjecture for symbolic systems with non-uniform structure. (12th September 2022)

• Record Type: Journal Article
• Authors: Ji, Yong; Chen, Ercai; Lin, Zijie
• Is Part Of: Nonlinearity. Volume 35:Number 10(2022)
• Page Start: 5226
• Page End: 5248
• Publication Date: 2022-09-12
• Subjects: pointwise emergence -- topological pressure -- non-uniform structure; 37B10 -- 37B40; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac8a3a
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Recently, Kiriki, Nakano and Soma introduced a concept called pointwise emergence as a new quantitative perspective into the study of non-existence of averages for dynamical systems. In the present paper, we consider the set of points with high pointwise emergence for symbolic systems with non-uniform structure and prove that this set carries full topological pressure. For the proof of this result, we show that such systems have ergodic measures of arbitrary intermediate pressures.