Bi-shadowing of Quasi-semi-hyperbolic Pseudo-orbit

TL;DR

This paper introduces quasi-semi hyperbolic pseudo-orbits, proves their relation to quasi hyperbolicity under small errors, and demonstrates their bi-shadowing property, establishing periodicity.

Contribution

It defines quasi-semi hyperbolic pseudo-orbits and proves their properties, including bi-shadowing and periodicity, expanding the understanding of pseudo-orbit dynamics.

Findings

Quasi-semi hyperbolic pseudo-orbits imply quasi hyperbolicity with small errors.

Finite and infinite quasi-semi hyperbolic pseudo-orbits have the bi-shadowing property.

Bi-shadowing leads to the establishment of periodicity in these systems.

Abstract

In this paper, we introduce the concept of quasi-semi hyperbolic pseudo-orbits and prove that quasi-semi hyperbolicity implies quasi hyperbolicity provided the error magnitude are sufficiently small. We also have successively demonstrated that both finite quasi-hyperbolic pseudo-orbits and infinite quasi-semi hyperbolic pseudo-orbits possess the bi-shadowing property, and thus we establish the periodicity.