Variational structures for infinite transition orbits of monotone twist maps

TL;DR

This paper explores the variational structures of monotone twist maps, a special class of area-preserving maps, to construct infinite transition orbits using minimizing methods, advancing understanding of chaotic dynamics.

Contribution

It introduces a variational framework for monotone twist maps to generate infinite transition orbits, extending the application of minimizing methods in dynamical systems.

Findings

Defined a variational structure for monotone twist maps

Constructed infinite transition orbits via minimizing methods

Enhanced understanding of chaotic dynamics in area-preserving maps

Abstract

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of area-preserving maps, we define a special class of area-preserving maps called monotone twist maps. Variational structures determined from twist maps can be used for constructing characteristic trajectories of twist maps. Our goal is to define the variational structure such as giving infinite transition orbits through minimizing methods.