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On loops in the hyperbolic locus of the complex Hénon map and their monodromies
- Source :
- Physica D: Nonlinear Phenomena. 334:133-140
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
Abstract
- We prove John Hubbard’s conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex Henon map. In fact, we show that there exist several non-trivial loops in the locus which generate infinitely many mutually different monodromies. Furthermore, we prove that the dynamics of the real Henon map is completely determined by the monodromy of the complex Henon map, providing the parameter of the map is contained in the hyperbolic horseshoe locus.
- Subjects :
- Pure mathematics
Topological complexity
Mathematics::Dynamical Systems
Conjecture
Pruning front
010102 general mathematics
Symbolic dynamics
Statistical and Nonlinear Physics
Condensed Matter Physics
01 natural sciences
Nonlinear Sciences::Chaotic Dynamics
010101 applied mathematics
Hénon map
Mathematics::Algebraic Geometry
Monodromy
0101 mathematics
Locus (mathematics)
Henon map
Mathematics
Subjects
Details
- ISSN :
- 01672789
- Volume :
- 334
- Database :
- OpenAIRE
- Journal :
- Physica D: Nonlinear Phenomena
- Accession number :
- edsair.doi.dedup.....908817d0871c6764c30bce0f36460a15