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Density of recurrent points on invariant manifolds of symplectic and volume-preserving diffeomorphisms

Published online by Cambridge University Press:  19 June 2002

FERNANDO OLIVEIRA
FERNANDO OLIVEIRA
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627-Caixa Postal 702, 30161-970-Belo Horizonte-MG, Brazil (e-mail: fernando@mat.ufmg.br)
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Abstract

In this paper we consider symplectic and volume-preserving diffeomorphisms of compact manifolds, and prove that, C^{r} generically, 1\leq r\leq\infty, the invariant manifolds of hyperbolic periodic points contain a dense subset of recurrent points. As a consequence, each of these invariant manifolds is contained in its omega limit set, and its closure is a chain transitive set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 3 , June 2002 , pp. 925 - 934
Copyright
2002 Cambridge University Press

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