Limit Bi-Shadowing for Semi-Hyperbolic Systems
Dynamical Systems
2026-03-31 v1
Abstract
This paper investigates the shadowing properties in semi-hyperbolic systems. We introduce three classes of shadowing properties defined on families of manifolds, and prove that a semi-hyperbolic family possesses the bi-shadowing property, the limit bi-shadowing property, and the asymptotic bi-shadowing property under certain conditions. The proof strategy is to transform the shadowing problem into a fixed-point problem, and then apply the Brouwer fixed-point theorem to complete the verification.
Cite
@article{arxiv.2603.28539,
title = {Limit Bi-Shadowing for Semi-Hyperbolic Systems},
author = {Linying Cheng and Haiye Guo},
journal= {arXiv preprint arXiv:2603.28539},
year = {2026}
}