2012/08/21 by Rafaël Potrie, Rafael Potrie, Potrie, Rafael
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #History and Overview (math.HO) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #math.HO
paper · pdf · doi:10.48550/arxiv.1208.4394
Expanded version of talk given at a conference in Montevideo: http://imerl.fing.edu.uy/sdm2012/
arxiv created 2012/08/21 · openalex publication_date 2012/08/21 · arxiv updated 2015/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We will try to give an overview of one of the landmark results of Jorge Lewowicz: his classification of expansive homeomorphisms of surfaces. The goal will be to present the main ideas with the hope of giving evidence of the deep and beautiful contributions he made to dynamical systems. We will avoid being technical and try to concentrate on the tools introduced by Lewowicz to obtain these classification results such as Lyapunov functions and the concept of persistence for dynamical systems. The main contribution that we will try to focus on is his conceptual framework and approach to mathematics reflected by the previously mentioned tools and fundamentally by the delicate interaction between topology and dynamics of expansive homeomorphisms of surfaces he discovered in order to establish his result.