Twist maps of the annulus: an abstract point of view

TL;DR

This paper introduces an abstract angle concept for annulus twist maps and uses it to unify proofs of classical results on area-preserving positive twist maps through topological theorems.

Contribution

It presents a novel abstract angle framework that simplifies and unifies proofs of key properties of twist maps in the annulus.

Findings

Unified proofs of classical results on twist maps

Introduction of an abstract angle concept

Application of topological theorems to dynamical systems

Abstract

We introduce the notion of abstract angle at a couple of points defined by two radial foliations of the closed annulus. We use this notion to give unified proofs of some classical results on area preserving positive twist maps of the annulus by using the Lifting Theorem and the Intermediate Value Theorem.