High pointwise emergence and Katok's conjecture for systems with non-uniform structure

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 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.

References in corpus (2)

• Entropy and Emergence of Topological Dynamical Systems
• Highly irregular orbits for subshifts of finite type: large intersections and emergence