Pontos periódicos quase elípticos em sistemas dinâmicos conservativos
=== Our objective is analize some generic properties of conservative and symplectic dynamical systems. We will focus our atention in two results we consider particularly relevant: Pixton's theorem, which proves the existence of a residual set of diffeomorphisms in R2 for which every hyperbolic...
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| Format: | Others |
| Language: | Portuguese |
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Universidade Federal de Minas Gerais
2012
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| Online Access: | http://hdl.handle.net/1843/EABA-8YAT47 |
| Summary: | === Our objective is analize some generic properties of conservative and symplectic dynamical systems. We will focus our atention in two results we consider particularly relevant: Pixton's theorem, which proves the existence of a residual set of diffeomorphisms in R2 for which every hyperbolical periodic point has transverse homoclinic intersection; and a theorem by Newhouse, that proves the existence of a subset B Diffr!
(M) such that if f 2 B then every quasi-elliptic periodic point of f is the limit of transverse homoclinic points off. === Nesse trabalho vamos analisar algumas propriedades genéricas de sistemas dinâmicos conservativos ou simpléticos. Vamos provar em detalhes dois resultados que consideramos relevantes: o teorema de Pixton, que afirma existe um subconjunto residual do conjunto dos difeos em R2 para o qual todo ponto periódico hiperbólico possui
interseção homoclínica transversal; e o teorema de Newhouse que prova a existência de um subconjunto B Diffr! (M) tal que se f 2 B então todo ponto quase elíptico de f é também limite de pontos homoclínicos transversais de f. |
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