| Full text | |
| Author(s): |
Mendoza, Valentin
Total Authors: 1
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| Document type: | Journal article |
| Source: | REGULAR & CHAOTIC DYNAMICS; v. 27, n. 4, p. 15-pg., 2022-07-01. |
| Abstract | |
The complexity of a dynamical system exhibiting a homoclinic orbit is given by its dynamical core which, due to Cantwell, Conlon and Fenley, is a set uniquely determined in the isotopy class, up to a topological conjugacy, of the end-periodic map relative to that orbit. In this work we prove that a sufficient condition to determine the dynamical core of a homoclinic orbit of a Smale diffeomorphism on the 2-disk is the non-existence of bigons relative to this orbit. Moreover, we propose a pruning method for eliminating bigons that can be used to find a Smale map without bigons and hence for finding the dynamical core. (AU) | |
| FAPESP's process: | 10/20159-6 - Pruning theory and dynamics of the complex Hénon family |
| Grantee: | Juan Valentín Mendoza Mogollón |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |