Partial hyperbolicity and central shadowing

TL;DR

This paper investigates the shadowing property in partially hyperbolic dynamical systems, demonstrating that under certain conditions, pseudotrajectories can be closely approximated with controlled deviations along the central foliation.

Contribution

It introduces a new shadowing result for dynamically coherent partially hyperbolic diffeomorphisms using fixed point techniques.

Findings

Pseudotrajectories can be shadowed with jumps along the central foliation.

The proof employs the Tikhonov-Shauder fixed point theorem.

Results apply to dynamically coherent systems.

Abstract

We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.