Characterizations of dominated splitting system and its relation to hyperbolicity

TL;DR

This paper explores the relationship between dominated splitting and hyperbolicity in differentiable dynamics, providing new characterizations and criteria for identifying dominated splitting systems.

Contribution

It offers several equivalent characterizations of dominated splitting and establishes a criterion linking it to hyperbolicity, advancing theoretical understanding.

Findings

Equivalent characterizations of dominated splitting

A criterion for systems to exhibit dominated splitting based on hyperbolicity

Enhanced theoretical framework for analyzing differentiable dynamical systems

Abstract

Hyperbolicity and dominated splitting are two of the most important concepts in the global analysis of differentiable dynamics. In this paper we give several equivalent characterizations of the dominated splitting and in particular we show a criterion for dynamical systems being dominated splitting in terms of hyperbolicity.18 pages