Variational Structures for Infinite Transition Orbits of Monotone Twist Maps

Abstract

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the 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 prove the existence of an infinite transition orbit, which represents an oscillating orbit between fixed points infinite times, through minimizing methods.