Abstract |
We discuss the existence of foliations that are invariant under the
dynamics for systems that are isotopic to Anosov diffeomorphisms.
Specifically, we examine partially hyperbolic diffeomorphisms with one
dimensional center that are isotopic to a hyperbolic toral automorphism and
contained in a connected component. We show in this case there is a center
foliation. We will also discuss more general cases where there is a weak
form of hyperbolicity called a dominated splitting. This is joint work with
Jerome Buzzi, Rafael Potrie, and Martin Sambarino.
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