The wild Fox-Artin arc in invariant sets of dynamical systems

TL;DR

This paper explores the emergence of the wild Fox-Artin arc within dynamical systems, demonstrating its role as an invariant manifold and heteroclinic intersection, highlighting the deep connection between topology and dynamics.

Contribution

It reveals how the wild Fox-Artin arc appears naturally in dynamical systems as an invariant structure, bridging topology and qualitative dynamics.

Findings

Wild Fox-Artin arc appears as an invariant manifold

It occurs as a heteroclinic intersection

Connects topology with dynamical systems theory

Abstract

The modern qualitative theory of dynamical systems is thoroughly intertwined with the fairly young science of topology. Strange and even bizarre constructions of topology are found sooner or later in dynamics of discrete or continuous dynamical systems. In the present paper we show that the wild Fox-Artin arc naturally emerges in dynamics as an invariant manifold of a fixed point and as a heteroclinic intersection.