On sufficient conditions for the transitivity of homeomorphisms
Abstract
We derive a necessary and sufficient condition for a homeomorphism with the shadowing property to be topologically transitive: to have an invariant subset , dense in the non-wandering set, where the barycenter property holds. To elucidate its dynamical nature, we compare this condition with other properties known to be sufficient for an Anosov diffeomorphism to be topologically transitive. We also describe the interior of the set of diffeomorphisms which comply with this condition, discuss examples with a variety of dynamics and present some applications of interest.
Keywords
Cite
@article{arxiv.2410.12958,
title = {On sufficient conditions for the transitivity of homeomorphisms},
author = {Maria Carvalho and Vinícius Coelho and Luciana Salgado},
journal= {arXiv preprint arXiv:2410.12958},
year = {2026}
}
Comments
37 pages, no figures, minor typos corrections and addition of comments on necessity of isolated points assumption in the text, addition of a new financial support reference. To appear in Dynamical Systems