Action and rotation number of periodic orbits of area-preserving annulus diffeomorphisms

TL;DR

This paper investigates the properties of periodic orbits in area-preserving surface diffeomorphisms, focusing on the action function and rotation numbers, and extends recent results to establish the existence of orbits with specific action and rotation values.

Contribution

It generalizes recent work by proving the existence of periodic orbits with prescribed action and rotation numbers in area-preserving surface diffeomorphisms.

Findings

Existence of periodic orbits with specific action values

Existence of periodic orbits with prescribed rotation numbers

Extension of previous results to broader classes of diffeomorphisms

Abstract

We study periodic orbits for area-preserving surface diffeomorphisms, particularly some global properities related to the action function and rotation numbers. We generalize recent works of Machel Hutchings [4], proving the existence of periodic orbits with certain action and rotation values.