2023/07/05 by Maria Carvalho, Carvalho, Maria, V. S. Coelho +3
Mathematics · #37A30 #37C10 #37C40 #37D20 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2307.02562
openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.