Dynamical coherence and center bunching
Keith Burns Amie Wilkinson
This paper discusses relationships among the basic notions that have been important in recent investigations of the ergodicity of volume-preserving partially hyperbolic diffeomorphisms. In particular we survey the possible definitions of dynamical coherence and discuss the relationship between dynamical coherence and center bunching.
keywords: partial hyperbolicity stable ergodicity. dynamical coherence center bunching
$C^1$-generic conservative diffeomorphisms have trivial centralizer
Christian Bonatti Sylvain Crovisier Amie Wilkinson
We prove that the spaces of $C^1$ symplectomorphisms and of $C^1$ volume-preserving diffeomorphisms of connected manifolds contain residual subsets of diffeomorphisms whose centralizers are trivial.
keywords: Trivial centralizer trivial symmetries $C^1$ generic properties.
Hölder foliations, revisited
Charles Pugh Michael Shub Amie Wilkinson
We investigate transverse Hölder regularity of some canonical leaf conjugacies in normally hyperbolic dynamical systems and transverse Hölder regularity of some invariant foliations. Our results validate claims made elsewhere in the literature.
keywords: normal hyperbolicity invariant foliations H\"older regularity of foliations. Partial hyperbolicity

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