Quasi-energy function for diffeomorphisms with wild separatrices

Details Quasi-energy function for diffeomorphisms with wild separatrices Quasi-energy function for diffeomorphisms with wild separatrices

2008-10-23

arxiv.org/abs/0810.4260v1

Mathematical Notes (transl. of Mat. Zametki) 86, 2 (2009) 163-170

Mathematics

Geometric Topology

Scientific paper

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.

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