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Kupka–Smale diffeomorphisms at the boundary of uniform hyperbolicity: a model
- Source :
- Nonlinearity. 30:3895-3931
- Publication Year :
- 2017
- Publisher :
- IOP Publishing, 2017.
-
Abstract
- We construct an explicit example of a family of non-uniformly hyperbolic diffeomorphisms, at the boundary of a set of uniformly hyperbolic systems, with one orbit of cubic heteroclinic tangency. One of the leaves involved in this heteroclinic tangency is periodic, and there is a Cantor set of choices of the second one. For a non-countable subset of these choices, the second leaf is not periodic and the diffeomorphism is Kupka–Smale: every periodic point is hyperbolic and the intersections of stable and unstable leaves of periodic points are transverse. The bifurcating system is Holder-conjugated to a subshift of finite type; thus every Holder potential admits a unique equilibrium state associated with it.
- Subjects :
- Pure mathematics
Mathematics::Dynamical Systems
Thermodynamic equilibrium
Applied Mathematics
010102 general mathematics
General Physics and Astronomy
Periodic point
Tangent
Boundary (topology)
Statistical and Nonlinear Physics
Subshift of finite type
01 natural sciences
Cantor set
0103 physical sciences
010307 mathematical physics
Diffeomorphism
0101 mathematics
Orbit (control theory)
Mathematical Physics
Mathematics
Subjects
Details
- ISSN :
- 13616544 and 09517715
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- Nonlinearity
- Accession number :
- edsair.doi...........61098ee5577e2a57d70598fd362dfc8d