Quasi-shadowing property for nonuniformly partially hyperbolic systems

Gang Liao; Xuetong Zu

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arXiv · 2501.03071

Quasi-shadowing property for nonuniformly partially hyperbolic systems

Gang Liao·Xuetong Zu

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Abstract

In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+\alpha}$ 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.

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BibTeX RIS

Gang Liao, Xuetong Zu. 2025-01-06. Quasi-shadowing property for nonuniformly partially hyperbolic systems. https://arxiv.org/abs/2501.03071

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