Topological methods in surface dynamics: from the Hénon family to torus rotation sets
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Pruning theory in the Hénon family.
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| Author(s): |
Juan Valentin Mendoza Mogollon
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2011-02-17 |
| Examining board members: |
André Salles de Carvalho;
Philip Lewis Boyland;
Daniel Smania Brandão;
Isabel Lugão Rios;
Fabio Armando Tal
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| Advisor: | André Salles de Carvalho |
| Abstract | |
Pruning is originally a way of giving a topological description of the dynamics of families of surface homeomorphisms. A diferentiable pruning theory is developed here. First pruning discs and the pruning theorem are presented for Smale\'s horseshoe, which is the paradigmatic chaotic dynamical system in dimension 2. Then this is generalized to hyperbolic surface difeomorphisms. This is then combined with complex and numerical techniques to give a computer assisted proof of the Pruning Front Conjecture for certain open sets of (real) parameters in the Hénon family. (AU) | |