V. Z. Grines, E. V. Zhuzhoma, V. S. Medvedev, “New relations for Morse–Smale systems with trivially embedded one-dimensional separatrices”, Mat. Sb., 2003, Volume 194, Number 7,Pages <nobr>25

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New relations for Morse–Smale systems with trivially embedded one-dimensional separatrices

V. Z. Grines^a, E. V. Zhuzhoma^b, V. S. Medvedev^c

^a Nizhnii Novgorod State Agricultural Academy
^b Nizhny Novgorod State Technical University
^c Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: New relations are established between the periodic structure of Morse–Smale systems (flows or diffeomorphisms) and the genus of Heegaard splittings of the supporting manifold. A sharp lower estimate is found for the number of non-closed heteroclinic curves of certain Morse–Smale diffeomorphisms on lens spaces.

UDC: 517.9+513.83

MSC: Primary 37D15, 37C25; Secondary 57N10

Received: 12.09.2001 and 23.12.2002

DOI: 10.4213/sm751