A new concept of local metric entropy for finite-time nonautonomous dynamical systems

TL;DR

This paper introduces a local finite-time entropy concept for nonautonomous dynamical systems, deriving formulas and demonstrating applications in detecting dynamical structures like Lagrangian coherent structures.

Contribution

It proposes a novel local finite-time entropy measure, extending classical metric entropy to nonautonomous systems and providing explicit formulas for 2-D cases.

Findings

Derived a finite-time version of Pesin's entropy formula.

Provided an explicit formula for finite-time entropy in 2-D systems.

Showed how to use finite-time entropy to detect Lagrangian coherent structures.

Abstract

We introduce a new concept of finite-time entropy which is a local version of the classical concept of metric entropy. Based on that, a finite-time version of Pesin's entropy formula and also an explicit formula of finite-time entropy for $2$-D systems are derived. We also discuss about how to apply the finite-time entropy field to detect special dynamical structures such as Lagrangian coherent structures.