Point fixe li\'e \`a une orbite p\'eriodique d'un diff\'eomorphisme de R2

TL;DR

This paper demonstrates how Nielsen fixed point theory can be applied to prove the existence of a fixed point linked to a given periodic orbit in a plane diffeomorphism.

Contribution

It introduces a novel application of Nielsen fixed point theory to establish fixed points associated with periodic orbits in planar diffeomorphisms.

Findings

Existence of a fixed point linked to a periodic orbit proven using Nielsen theory

Method applicable to diffeomorphisms of the plane with periodic orbits

Provides a theoretical framework connecting fixed points and periodic orbits

Abstract

Given a diffeomorphism of the plane, which has a periodic orbit, we show how Nielsen fixed point theory can be used to establish the existence of a fixed point which is linked with this periodic orbit.