Nondensity of orbital shadowing property in C^1-topology

TL;DR

This paper proves that the orbital shadowing property is not dense in the space of C^1-smooth dynamical systems on closed manifolds, using skew product methods.

Contribution

It establishes the nondensity of the orbital shadowing property in C^1-topology for discrete dynamical systems on closed manifolds.

Findings

Orbital shadowing property is not dense in C^1-topology.

Uses skew product method by Ilyashenko and Gorodetski.

Provides a rigorous proof of nondensity.

Abstract

The orbital shadowing property (OSP) of discrete dynamical systems on smooth closed manifolds is considered. Nondensity of OSP with respect to the C^1-topology is proved. The proof uses the method of skew products developed by Yu.S. Ilyashenko and A.S. Gorodetski.