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The paper is devoted to finding conditions to the existence of a self-indexing energy function for Morse-Smale diffeomorphisms on a 3manifold M3. These conditions involve how the stable and unstable manifolds of saddle points are embedded in the ambient manifold. We also show that the existence of a self-indexing energy function is equivalent to the… (More)

According to Pixton [8] there are Morse-Smale diffeomorphisms of S3 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 MorseSmale diffeomorphism as a Lyapunov function with the least number of critical points and construct a… (More)

This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from [3], [4], 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,… (More)

- V. Grines, O. Pochinka, E. Zhuzhoma
- I. J. Bifurcation and Chaos
- 2014

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