DCDS
Dynamical coherence and center bunching
Keith Burns Amie Wilkinson
Discrete & Continuous Dynamical Systems - A 2008, 22(1&2): 89-100 doi: 10.3934/dcds.2008.22.89
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
JMD
$C^1$-generic conservative diffeomorphisms have trivial centralizer
Christian Bonatti Sylvain Crovisier Amie Wilkinson
Journal of Modern Dynamics 2008, 2(2): 359-373 doi: 10.3934/jmd.2008.2.359
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.
JMD
Hölder foliations, revisited
Charles Pugh Michael Shub Amie Wilkinson
Journal of Modern Dynamics 2012, 6(1): 79-120 doi: 10.3934/jmd.2012.6.79
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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