Dendritations of Surfaces

2018/01/26 by Alfonso Artigue, Artigue, Alfonso · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1801.08783

openalex publication_date 2018/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• L-shadowing for the induced hyperspace homeomorphism

Related

• Dynamics of surface homeomorphisms Topological versions of the Leau-Fatou flower theorem and the stable manifold theorem
• Foliated Plateau problems, geometric rigidity and equidistribution of closed k-surfaces
• Foliations on non-metrisable manifolds II: contrasted behaviours
• Foliated Plateau problems and asymptotic counting of surface subgroups
• Singular Riemannian Foliations and the prescribing scalar curvature problem