Quasi-energy function for diffeomorphisms with wild separatrices

Viatcheslav Grines (1) , Francois Laudenbach (2) , Olga Pochinka (1)

1 department of mathematics, N. Novgorod State University
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: Morse-Smale diffeomorphism; Lyapunov function; Morse theory.; Morse theory

Domaines: Topologie géométrique [math.GT]

Viatcheslav Grines, Francois Laudenbach, Olga Pochinka. Quasi-energy function for diffeomorphisms with wild separatrices. Mathematical Notes (transl. of Mat. Zametki), 2009, 86 (2), pp.163-170. ⟨hal-00333484⟩