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Stability of accessibility

Published online by Cambridge University Press:  02 December 2003

Ph. DIDIER
Ph. DIDIER
Affiliation:
Avenida Don Carlos I, 124/4C, 1200 Santos, Lisbon, Portugal (e-mail: [email protected])
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Abstract

We give a partial answer to a question posed by C. Pugh and M. Shub in [PS2]. A partially hyperbolic diffeomorphism $f\in \mathit{Diff}^{2}(M)$ is accessible if every two points of M can be connected by a path which is piecewise in a stable or an unstable leaf. We prove that accessibility is open in $\mathit{Diff}^{2}(M)$ among the partially hyperbolic diffeomorphisms with one-dimensional center bundle.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 6 , December 2003 , pp. 1717 - 1731
Copyright
2003 Cambridge University Press

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