2024/07/09 by Sogo Murakami, Murakami, Sogo
Mathematics · Physics and Astronomy · #37C50 #37D20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2407.06588
openalex publication_date 2024/07/09 · openalex created_date 2024/07/12 · openalex updated_date 2026/07/28
Petrov and Pilyugin (2015) generalized a notion of C0 transversality of Sakai (1995) using smooth curves. Their definition involves only continuous maps from \mathbb Rn to a manifold, which is a purely topological one. They also provided a sufficient condition for the C0 transversality in terms of homological nature. In this paper, we prove that such a homological condition of Axiom A diffeomorphisms is sufficient for enjoying the shadowing property. Moreover, it is proved that the C0 transversality of Axiom A diffeomorphisms with codimension one basic sets implies the homological condition.