Multidimensional $C^0$ transversality and the shadowing property for Axiom A diffeomorphisms
Dynamical Systems
2024-07-10 v1
Abstract
Petrov and Pilyugin (2015) generalized a notion of transversality of Sakai (1995) using smooth curves. Their definition involves only continuous maps from to a manifold, which is a purely topological one. They also provided a sufficient condition for the 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 transversality of Axiom A diffeomorphisms with codimension one basic sets implies the homological condition.
Cite
@article{arxiv.2407.06588,
title = {Multidimensional $C^0$ transversality and the shadowing property for Axiom A diffeomorphisms},
author = {Sogo Murakami},
journal= {arXiv preprint arXiv:2407.06588},
year = {2024}
}