Partially hyperbolic diffeomorphisms with compact center
Andrey Gogolev - Department ofMathematical Sciences, The State University of New York, Binghamton, NY 13902, United States (email)
Let $f\colon M\to M$ be a partially hyperbolic diffeomorphism such
that all of its center leaves are compact. We prove that Sullivan's
example of a circle foliation that has arbitrary long leaves cannot be
the center foliation of $f$. This is proved by thorough study of the
accessible boundaries of the center-stable and the center-unstable
Keywords: Partially hyperbolic diffeomorphism, skew product, compact foliation,
Reeb stability, Wada Lakes, accessible boundary, Anosov homeomorphism, holonomy.
Received: November 2011; Revised: February 2012; Published: March 2012.