On entropy of Φ-irregular and Φ-level sets in maps with the shadowing property

2019/09/18 by Magdalena Foryś-Krawiec, Jiří Kupka, Foryś-Krawiec, Magdalena +5
Chemistry · Mathematics · #Chromatography in Natural Products #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1909.08463

openalex publication_date 2019/09/18 · openalex created_date 2019/09/26 · openalex updated_date 2026/07/28

Abstract

We study the properties of Φ-irregular sets (sets of points for which the Birkhoff average diverges) in dynamical systems with the shadowing property. We estimate the topological entropy of Φ-irregular set in terms of entropy on chain recurrent classes and prove that Φ-irregular sets of full entropy are typical. We also consider Φ-level sets (sets of points whose Birkhoff average is in a specified interval), relating entropy they carry with the entropy of some ergodic measures. Finally, we study the problem of large deviations considering the level sets with respect to reference measures.

Citations

• Topological entropy for noncompact sets
• Pseudo-orbit shadowing in the family of tent maps
• Irregular sets, the 𝛽-transformation and the almost specification property

Related

• Metric mean dimension of irregular sets for maps with shadowing
• On the irregular points for systems with the shadowing property
• Entropy of irregular points that are not uniformly hyperbolic
• Some results on shadowing and local entropy properties of dynamical systems
• On the structure of the Birkhoff-irregular set for subshifts of finite type