Quasi-shadowing property for nonuniformly partially hyperbolic systems
Dynamical Systems
2025-01-07 v1
Abstract
In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a diffeomorphism, which is adaptive to the movement of the pseudo-orbit. Moreover, the quasi-specification property and quasi-closing property are also investigated. As an application of quasi-closing property, we extend Katok's reslut on the growth of periodoc orbits for hyperbolic ergodic measure to any ergodic measure: the number of quasi-periodic points grows exponentially at least the metric entropy.
Cite
@article{arxiv.2501.03071,
title = {Quasi-shadowing property for nonuniformly partially hyperbolic systems},
author = {Gang Liao and Xuetong Zu},
journal= {arXiv preprint arXiv:2501.03071},
year = {2025}
}