Year: 2025
Type: preprint
Abstract: In this paper, we establish a new quasi-shadowing property for any nonuiformly partially hyperbolic set of a $C^{1+α}$ 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.
Source: arXiv (Cornell University)
Authors: Liao, Gang, Zu, Xuetong
Institution: Soochow University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G3250800360, G5886365578
OpenAlex ID: W4406123533