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On the integrability of intermediate distributions for Anosov diffeomorphisms†

Published online by Cambridge University Press:  19 September 2008

M. Jiang ,
Ya B. Pesin  and
R. de la Llave
M. Jiang
Affiliation:
Department of Mathematics, Penn State University, University Park PA 16802, USA (e-mail: [email protected] and [email protected])
Ya B. Pesin
Affiliation:
Department of Mathematics, Penn State University, University Park PA 16802, USA (e-mail: [email protected] and [email protected])
R. de la Llave
Affiliation:
Department of Mathematics, University of Texas, Austin TX 78712-1802, USA (e-mail: [email protected])
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Abstract

We study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of a C∞-Anosov diffeomorphism on a three-dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 2 , April 1995 , pp. 317 - 331
Copyright
Copyright © Cambridge University Press 1995

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