Avila, Artur, Bochi, Jairo, Wilkinson, Amie
We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns--Wilkinson and Avila--Santamaria--Viana. Combining this new...
The cohomological equation for partially hyperbolic diffeomorphisms (2008)
We establish a theory for the existence and regularity of solutions to the cohomological equation over an accessible, partially hyperbolic diffeomorphism. As a by-product of our techniques, we show...
The C1 generic diffeomorphism has trivial centralizer (2008)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.
The C1 generic diffeomorphism has trivial centralizer (2008)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
The C1 generic diffeomorphism has trivial centralizer (2008)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
HYPERBOLIC DIFFEOMORPHISMS (2008)
Amie Wilkinson, Amie Wilkinson
2. Partial hyperbolicity and bunching conditions 10
Boris Hasselblatt, Amie Wilkinson
Abstract. We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems in terms of contraction and expansion rates and prove optimality in a strong sense: we...
When An Infinitely-Renormalizable Endomorphism Of The Interval Can Be Smoothed (2007)
Charles Tresser, Amie Wilkinson
Let K be a closed subset of a smooth manifold M , and let f : K ! K be a continuous selfmap of K. We say that f is smoothable if it is conjugate to the restriction of a smooth map by a homeomorphism...
open and dense set of accessible diffeomorphisms. (2007)
Dmitry Dolgopyat, Amie Wilkinson
We prove that in the space of all C
Wilkinson's work was partly funded by NSF Grant #DMS-0100314. (2007)
Charles Pugh, Michael Shub, Amie Wilkinson, C. Pugh, M. Shub, A. Wilkinson
A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of dierentiability of its invariant splitting. In this paper, we show that often partial derivatives of the...
C1-generic conservative diffeomorphisms have trivial centralizer (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial....
Local density of diffeomorphisms with large centralizers (2007)
Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia, Wilkinson, Amie
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is...
The centralizer of a C1 generic diffeomorphism is trivial (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact connected manifold...
Centralizers of C^1-generic diffeomorphisms (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On...
The centralizer of a C1 generic diffeomorphism is trivial (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
In this announcement, we describe the solution in the C1 topology to a question asked by S. Smale on the genericity of trivial centralizers: the set of diffeomorphisms of a compact connected manifold...
Local density of diffeomorphisms with large centralizers (2007)
Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia, Wilkinson, Amie
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is...
C1-generic conservative diffeomorphisms have trivial centralizer (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial....
C1-generic conservative diffeomorphisms have trivial centralizer (2007)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial....
Local density of diffeomorphisms with large centralizers (2007)
Bonatti, Christian, Crovisier, Sylvain, Vago, Gioia, Wilkinson, Amie
Given any compact manifold M, we construct a non-empty open subset O of the space of C^1-diffeomorphisms of M and a dense subset D of O such that the centralizer of every diffeomorphism in D is...
Centralizers of C^1-generic diffeomorphisms (2006)
Bonatti, Christian, Crovisier, Sylvain, Wilkinson, Amie
On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On...
On the ergodicity of partially hyperbolic systems (2005)
Pugh and Shub have conjectured that essential accessibility implies ergodicity, for a $C^2$, partially hyperbolic, volume-preserving diffeomorphism. We prove this conjecture under a mild center...
Global rigidity of solvable group actions on S^1 (2003)
Burslem, Lizzie, Wilkinson, Amie
In this paper we find all solvable subgroups of Diff^omega(S^1) and classify their actions. We also investigate the C^r local rigidity of actions of the solvable Baumslag-Solitar groups on the...
Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds (2003)
Christian Bonatti, Amie Wilkinson
The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T², perturbations of the...
Abundance of Stable Ergodicity (2003)
Christian Bonatti, Carlos Matheus, Marcelo Viana, Amie Wilkinson
We consider the set PH! (M) of volume preserving partially hyperbolic dieomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even...
Random versus deterministic exponents in a rich family of diffeomorphisms (2002)
Ledrappier, Francois, Shub, Michael, Simo, Carles, Wilkinson, Amie
We study, both numerically and theoretically, the relationship between the random Lyapunov exponent of a family of area preserving diffeomorphisms of the 2-sphere and the mean of the Lyapunov...
Partial differentiability of invariant splittings (2002)
Pugh, Charles, Shub, Michael, Wilkinson, Amie
A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial derivatives of the...
Absolutely singular dynamical foliations (2000)
Ruelle, David, Wilkinson, Amie
We show that for the C^1-open set of partially hyperbolic diffeomorphisms constructed in (M. Shub and A. Wilkinson, "Pathological foliations and removable zero exponents," Invent. math. 139 (2000) 3,...
Stably Ergodic Approximation: Two Examples (2000)
It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volume-preserving, partially hyperbolic diffeomorphisms of a compact manifold. In this paper we deal...
Prevalence of non-Lipschitz Anosov foliations. Ergodic Theory Dynam (1999)
Boris Hasselblatt, Amie Wilkinson
To the memory of Gunnar Hasselblatt, 19.8.1928--12.7.1997 Abstract. We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems and give open dense sets of...
Recent results about stable ergodicity (1999)
Keith Burns, Charles Pugh, Michael Shub, Amie Wilkinson
The ergodic theory of uniformly hyperbolic, or Axiom A, dieomorphisms has been studied extensively, beginning with the pioneering work of Anosov, Sinai,
Pathological Foliations and Removable Zero Exponents (1999)
this paper was motivated by the question of whether nonuniform hyperbolicity is dense among a large class of dieomorphisms. As a curious by-product of our construction, we prove that a pathological...
Stable Ergodicity of Skew Products (1999)
Stable ergodicity is dense among compact Lie group extensions of Anosov diffeomorphisms of compact manifolds. Under the additional assumption that the base map acts on an infranilmanifold, an...
Prevalence of non-Lipschitz Anosov foliations. Ergodic Theory Dynam (1999)
Boris Hasselblatt, Amie Wilkinson
Abstract. We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems and give open dense sets of codimension one systems where this regularity is not exceeded as...
A stably Bernoullian diffeomorphism that is not Anosov (1998)
this paper we construct new examples of diffeomorphisms with robust statistical properties. Our interest in these examples arose from the insight they might give into a collection of natural,...
Stable Ergodicity and Anosov Flows (1998)
Keith Burns, Charles Pugh, Amie Wilkinson
In this note we prove that if M is a 3-manifold and ' t : M ! M is a C 2 , volume-preserving Anosov flow, then the time-1 map ' 1 is stably ergodic if and only if ' t is not a...
Prevalence of non-Lipschitz Anosov foliations Elektronische Daten (1997)
Hasselblatt, Boris, Wilkinson, Amie
Institute for Mathematical Research
Stable Ergodicity of the Time-One Map of a Geodesic Flow (1997)
this paper, we extend this result to variable negative curvature. More precisely, our Main Theorem states:
Prevalence of non-Lipschitz Anosov foliations (1997)
Boris Hasselblatt, Amie Wilkinson
. We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems and give open dense sets of codimension one systems where this regularity is not exceeded as well as...
Prevalence Of Non-Lipschitz Anosov Foliations (1997)
Boris Hasselblatt, AMIE WILKINSON
. We give sharp regularity results for the invariant subbundles of hyperbolic dynamical systems in terms of contraction and expansion rates and prove optimality in a strong sense: we construct open...
Prevalence of Non-Lipschitz Anosov Foliations (1997)
Boris Hasselblatt, Amie Wilkinson
. We give sharp regularity results for the invariant distributions of hyperbolic dynamical systems in terms of eigenvalue data at periodic points and prove optimality in a strong sense: we construct...