Dendritations of Surfaces

TL;DR

This paper introduces dendritations of surfaces, a generalized foliation concept in metric spaces, with applications in dynamical systems and new forms of expansivity.

Contribution

It develops a novel framework for dendritations on surfaces, extending foliated manifold theory to metric spaces and applying it to dynamical systems analysis.

Findings

Dendritations provide a new way to decompose surfaces into dendrites.

Applications include modeling stable and unstable sets in dynamical systems.

New forms of expansivity are introduced for these structures.

Abstract

In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions into dendrites. Applications are given in modeling stable and unstable sets of topological dynamical systems. For this purpose new forms of expansivity are defined.