Dynamically ordered energy function for Morse-Smale diffeomorphisms on 3-manifolds

Autor: Grines, Viatcheslav, Laudenbach, Francois, Pochinka, Olga
Přispěvatelé: Department of mathematics, N. Novgorod State University, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), RFBR of Russian Academy No 11-01-007300 Russian Federation No 11.G34.31.0039, ANR-08-BLAN-0291,Floer Power,Applications des courbes holomorphes en géométrie symplectique et de contact(2008)
Jazyk: angličtina
Rok vydání: 2011
Předmět:
Zdroj: Proceedings of the Steklov Institute of Mathematics
Proceedings of the Steklov Institute of Mathematics, MAIK Nauka/Interperiodica, 2012, 278, pp.1-14
ISSN: 0081-5438
1531-8605
Popis: This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which fits well dynamics of diffeomorphism. The paper is devoted to finding conditions to the existence of such an energy function, that is, a function whose set of critical points coincides with the non-wandering set of the considered diffeomorphism. We show that the necessary and sufficient conditions to the existence of a dynamically ordered energy function reduces to the type of embedding of one-dimensional attractors and repellers of a given Morse-Smale diffeomorphism on a closed 3-manifold.
Databáze: OpenAIRE
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