On the topological classification of dynamics of inner mappings on the regular components of the wandering set with a special attracting boundary

TL;DR

This paper provides a topological classification method for inner mappings on certain invariant components of wandering sets with attracting boundaries, using distinguishing graphs to determine conjugacy.

Contribution

It introduces a classification framework based on distinguishing graphs that characterizes topological conjugacy of inner mappings with the same degree.

Findings

Topological conjugacy is characterized by the equivalence of distinguishing graphs.

Inner mappings of the same degree are equivalent if their graphs are equivalent.

The classification applies to fully invariant regular components with attracting boundaries.

Abstract

The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner mappings of the same degree are topologically equivalent on their fully invariant regular components of a certain class if and only if their distinguishing graphs are equivalent.