Non-stationary normal coordinates on neighborhoods of Pesin stable manifolds

TL;DR

This paper develops non-stationary normal coordinates near Pesin stable manifolds, extending previous work to better describe the fractal geometry of stable and unstable foliations in smooth dynamical systems.

Contribution

It introduces a new framework for non-stationary normal coordinates around Pesin stable manifolds, extending existing methods to include jets in the normal directions.

Findings

Provides a natural extension of non-stationary normal coordinates to Pesin stable manifolds.

Facilitates the analysis of fractal geometric structures in dynamical systems.

Enhances understanding of stable and unstable foliations in smooth systems.

Abstract

We construct non-stationary normal coordinates in a neighborhood of Pesin stable manifolds \cite{Pesin}. This construction is a natural extension, via jets in the normal directions, of the non-stationary normal coordinates on stable manifolds introduced by Guysinsky and Katok. We emphasize that this extension provides a useful framework for describing the fractal geometric structures of stable and unstable foliations in smooth dynamical systems.