Pseudo-B\"ottcher components of the wandering set of inner mappings

TL;DR

This paper investigates the topological structure of Pseudo-Böttcher components within the wandering set of certain inner mappings on compact surfaces, revealing a greater diversity than in homeomorphisms.

Contribution

It characterizes the topological types of Pseudo-Böttcher invariant components for non-invertible inner mappings, expanding understanding beyond known homeomorphism cases.

Findings

Classified possible topological types of invariant components

Demonstrated greater diversity compared to homeomorphisms

Provided new insights into the structure of wandering sets

Abstract

This article explores the topology of Pseudo-B\"ottcher totally invariant connected components of the wandering set in dynamical systems generated by on-invertible inner (open surjective isolated) mappings of compact surfaces. We describe the possible topological types of these invariant connected subsets, which are more diverse then corresponding components of homeomorphisms.