Quasi-energy function for diffeomorphisms with wild separatrices

Viatcheslav Grines; Francois Laudenbach; Olga Pochinka

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arXiv · 0810.4260

Quasi-energy function for diffeomorphisms with wild separatrices

Viatcheslav Grines·Francois Laudenbach·Olga Pochinka

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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.

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BibTeX RIS

Viatcheslav Grines, Francois Laudenbach, Olga Pochinka. 2008-10-23. Quasi-energy function for diffeomorphisms with wild separatrices. https://arxiv.org/abs/0810.4260

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