Energy function and topological classification of Morse-Smale flows on surfaces

E. Ya. Gurevich, E. D. Kurenkov

State University – Higher School of Economics

Abstract: We introduce the definition of consistent equivalence of energy Morse-Bott functions for Morse-Smale flows on surfaces and state that consistent equivalence of that functions is necessary and sufficient condition for such flows.

Keywords: structurally stable flows on surfaces, Morse-Smale flows, Lyapunov function, topological equivalence, topological classification.

UDC: 517.9

Received: 17.07.2015

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