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Stable weakly shadowable volume-preserving systems are volume-hyperbolic
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Orientador(es)
Resumo(s)
We prove that any C^1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F . Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.
Descrição
Palavras-chave
Weak shadowing Dominated splitting Hyperbolicity
Contexto Educativo
Citação
Bessa, M., Lee, M. & Vaz, S. Stable weakly shadowable volume-preserving systems are volume-hyperbolic. Acta. Math. Sin.-English Ser. 30, 1007–1020 (2014)
Editora
Springer