Work

On the completely irregular set for systems with the shadowing property

Year: 2023

Type: preprint

Abstract: We prove that the completely irregular set is Baire generic for every non-uniquely ergodic transitive continuous map which satisfies the shadowing property and acts on a compact metric space without isolated points. We also show that, under the previous assumptions, the orbit of any completely irregular point is dense. Afterwards, we analyze the connection between transitivity and the shadowing property, draw a few consequences of their joint action within the family of expansive homeomorphisms, and discuss several examples to test the scope of our results.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2307.02562

Authors: Carvalho, Maria, Coelho, Vinícius, Salgado, Luciana

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Fundação para a Ciência e a Tecnologia, Centro de Matemática Universidade do Porto

Awards: G1840770272, G2584274330, G2763643389, G29316538, Centro de Matemática da Universidade do Porto, Médias e Extremos em Sistemas Dinâmicos, G5157461147, G5341562090, Centro de Matemática da Universidade do Porto, G5517433818, G8367123964

OpenAlex ID: W4383604368

Cites:

Cited by:

Related to: 10