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

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.