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Quasi-energy function for diffeomorphisms with wild separatrices
- 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.
- Subjects :
- Lyapunov function
Class (set theory)
Pure mathematics
Mathematics::Dynamical Systems
General Mathematics
010102 general mathematics
Mathematical analysis
Cobordism
Function (mathematics)
01 natural sciences
010101 applied mathematics
symbols.namesake
symbols
Diffeomorphism
0101 mathematics
Mathematics::Symplectic Geometry
Heegaard splitting
Saddle
Mathematics
Morse theory
Subjects
Details
- ISSN :
- 15738876 and 00014346
- Volume :
- 86
- Database :
- OpenAIRE
- Journal :
- Mathematical Notes
- Accession number :
- edsair.doi...........a6b5bbb5e1be9bc28402f0fa5d782c84