Hyperbolic sets exhibiting ¹-persistent homoclinic tangency for higher dimensions
By Masayuki Asaoka. 2007
47 citations recorded by the source corpus.
For any manifold of dimension at least three, we give a simple construction of a hyperbolic invariant set that exhibits C1-persistent homoclinic tangency. It provides an open subset of the space of C 1 -diffeomorphisms in which generic diffeomorphisms have arbitrary given growth of the number of attracting periodic orbits and admit no symbolic extensions.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/29aeddb7dc8f6c7a3030e3243e5d2d6fcd07eb94
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Generic family with robustly infinitely many sinks (2014, background): “onstruction of Newhouse worked for surface dieomorphisms and in the Cr-topology, r2. Another construction of Newhouse was done for Cr-dieomorphisms of n-manifold, for n3 and r1 [New80] (see also [Asa08]). Latter, Bonatti-Diaz constructed an example of hyperbolic set B of R3 with C1-robust homoclinic”
- Abundance of C 1 -robust homoclinic tangencies (2009, background): “ewhouse construction. Geometrical constructions using these kind of “thick” hyperbolic sets provide examples of systems with C1-robust heterodimensional cycles2 (see [3]) or C1-robust tangencies (see [28, 4]). But these constructions involve quite specific global dynamical configurations, thus they ca”