Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems

TL;DR

This paper explores the relationship between Lyapunov exponents and how the volume of boundary regions in phase space expands under dynamical systems, providing insights into system stability and chaos.

Contribution

It establishes a theoretical link between Lyapunov exponents and boundary volume growth, enhancing understanding of dynamical system behavior.

Findings

Lyapunov exponents correlate with boundary volume growth.

Boundary distortion can be quantified through volume expansion rates.

Results contribute to stability analysis of dynamical systems.

Abstract

We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.