2017/12/06 by В. З. Гринес, Grines, V. Z., О. V. Pochinka +3
Mathematics · #37-XX #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1712.02230
openalex publication_date 2017/12/06 · openalex created_date 2022/09/05 · openalex updated_date 2026/07/28
In this paper we give a complete topological classification of orientation preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS diffeomorphisms with relatively simple behaviour it was known that such a classification can be given through a directed graph, a three-colour directed graph or by a certain topological object, called a scheme. Here we will assign to any MS surface diffeomorphism a finite amount of data which completely determines its topological conjugacy class. Moreover, we show that associated to any abstract version of this data, there exists a unique conjugacy class of MS orientation preserving diffeomorphisms (on some orientation preserving surface). As a corollary we obtain a different proof that nearby MS diffeomorphisms are topologically conjugate.