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Zhurnal SVMO, 2014, Volume 16, Number 3, Pages 57–61 (Mi svmo495)  

In Middle Volga Mathematical Society

Energy function as a complete topological invariant for gradient-like cascades on surfaces

V. E. Kruglova, O. V. Pochinkab

a N. I. Lobachevski State University of Nizhni Novgorod
b National Research University "Higher School of Economics", Nizhny Novgorod Branch

Abstract: In this paper we consider dynamical systems with discrete time generated by iterations of a gradient-like diffeomorphism of a surface whose non-wandering set consists of fixed points of positive type orientation. We prove that the class of topological conjugacy of such a system is completely determined by equivalence class of its energy Morse function.

Keywords: energy function, gradient-like diffeomorphism

References: PDF file   HTML file
UDC: 517.9
Received: 27.12.2014

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