Sternberg linearization theorem for skew products

TL;DR

This paper introduces a linearization theorem for skew products, showing that under certain conditions, these systems can be normalized to a form with linear fiber maps, with conjugacies being Hölder continuous.

Contribution

The paper establishes a new normalization theorem for skew products, extending linearization techniques to this class and analyzing the regularity of conjugacies in the smooth case.

Findings

Normal form is a skew product with linear fiber maps

Conjugacy is Hölder continuous in the smooth case

Applicable to perturbations and attractor properties

Abstract

We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older continuous with respect to the base. The normalization theorem mentioned above may be applied to perturbations of skew products and to the study of new persistent properties of attractors.