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

Yan He, Meihua Jin

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.

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

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.

Paper Structure

This paper contains 4 sections, 4 theorems, 126 equations.

Table of Contents

  1. Introduction
  2. Quasi-semi hyperbolicity implies quasi hyperbolicity
  3. Bi-shadowing of Finite Quasi-semi-hyperbolic pseudo-orbit
  4. Bi-Shadowing of Infinite Quasi-semi-hyperbolic Pseudo-orbit and Periodic Bi-Shadowing

Key Result

Lemma 3.1

Given $\lambda\in (0,1)$, any $\lambda$-quasi-hyperbolic pair of sequences $\{a_{i},b_{i}\}_{i=1}^{n}$ has a well-adapted sequence $\{c_{i}\}_{i=1}^{n}$.

Theorems & Definitions (20)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Remark 2.1
  • proof
  • Definition 3.1
  • Definition 3.2
  • Lemma 3.1
  • Remark 3.1
  • Definition 3.3
  • ...and 10 more