V. Z. Grines, S. H. Kapkaeva, O. V. Pochinka, “A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces”, Mat. Sb., 2014, Volume 205, Number 10,Pages <nobr>19

This article is cited in 17 papers

A three-colour graph as a complete topological invariant for gradient-like diffeomorphisms of surfaces

V. Z. Grines^a, S. H. Kapkaeva^b, O. V. Pochinka^a

^a N. I. Lobachevski State University of Nizhni Novgorod
^b Ogarev Mordovia State University, Saransk

Abstract: In a paper of Oshemkov and Sharko, three-colour graphs were used to make the topological equivalence of Morse-Smale flows on surfaces obtained by Peixoto more precise. In the present paper, in the language of three-colour graphs equipped with automorphisms, we obtain a complete (including realization) topological classification of gradient-like cascades on surfaces.
Bibliography: 25 titles.

Keywords: Morse-Smale diffeomorphism, gradient-like diffeomorphism, three-colour graph, topological classification.

UDC: 517.938

MSC: Primary 37D15; Secondary 37C05, 37C15, 37E30

Received: 15.01.2014

DOI: 10.4213/sm8328