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Compact dynamical foliations

Published online by Cambridge University Press:  04 August 2014

PABLO D. CARRASCO
PABLO D. CARRASCO*
Affiliation:
I.M.P.A., Estrada Dona Castorina 110 CEP 22360 420, Rio de Janeiro, Brazil email pdcarrasco@gmail.com
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Abstract

According to the work of Dennis Sullivan [A counterexample to the periodic orbit conjecture. Publ. Math. Inst. Hautes Études Sci. 46 (1976), 5–14], there exists a smooth flow on the five-sphere all of whose orbits are periodic, although there is no uniform bound on their periods. The question addressed in this article is whether these type of examples can occur in the partially hyperbolic context. That is, does there exist a partially hyperbolic diffeomorphism of a compact manifold such that all the leaves of its center foliation are compact but there is no uniform bound for their volumes? We develop tools to attack the previous question and show that it has a negative answer provided that all periodic leaves have finite holonomy.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 8 , December 2015 , pp. 2474 - 2498
Copyright
© Cambridge University Press, 2014 

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