Minimization and Hyperbolicity

TL;DR

This paper explores how the properties of locally minimizing orbits in time-dependent Lagrangian systems relate to the hyperbolic nature of the flow, providing insights into the system's stability and dynamics.

Contribution

It establishes a connection between local minimization in Lagrangian systems and hyperbolicity, advancing understanding of their dynamical behavior.

Findings

Identifies conditions linking minimizers to hyperbolic flows

Provides criteria for hyperbolicity based on orbit minimization

Enhances theoretical framework for analyzing Lagrangian dynamics

Abstract

In this paper we study the relationship between the strict locally minimizing orbits for time dependent lagrangian systems and hyperbolicity properties of the corresponding lagrangian flow.