On Strongly Irregular Points of a Brouwer Homeomorphism Embeddable in a Flow

Abstract

We study the set of all strongly irregular points of a Brouwer homeomorphism $f$ which is embeddable in a flow. We prove that this set is equal to the first prolongational limit set of any flow containing $f$. We also give a sufficient condition for a class of flows of Brouwer homeomorphisms to be topologically conjugate.