Existence de points fixes enlac\'es \`a une orbite p\'eriodique d'un hom\'eomorphisme du plan

TL;DR

This paper proves that for certain plane homeomorphisms with contracting properties, every periodic orbit is linked to a fixed point with a nonzero linking number, highlighting a topological relationship between fixed points and periodic orbits.

Contribution

It establishes the existence of fixed points with nonzero linking numbers for all periodic orbits under specific contracting conditions, extending understanding of orbit-fixed point relationships.

Findings

Fixed points with nonzero linking numbers exist for all periodic orbits.

The results apply to orientation-preserving homeomorphisms with contracting f-Id.

The work generalizes linking properties in planar dynamical systems.

Abstract

Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic orbit.