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Quasi-energy function for diffeomorphisms with wild separatrices

Authors :
Olga V. Pochinka
Francois Laudenbach
V. Z. Grines
Source :
Mathematical Notes. 86:163-170
Publication Year :
2009
Publisher :
Pleiades Publishing Ltd, 2009.

Abstract

According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the least number of critical points and construct a quasi-energy function for any diffeomorphism from some class of Morse-Smale diffeomorphisms on the 3-sphere.

Details

ISSN :
15738876 and 00014346
Volume :
86
Database :
OpenAIRE
Journal :
Mathematical Notes
Accession number :
edsair.doi...........a6b5bbb5e1be9bc28402f0fa5d782c84