Wilkinson, Amie 1968
Overview
Works:  10 works in 31 publications in 1 language and 248 library holdings 

Genres:  Academic theses 
Roles:  Editor, Author, Other 
Publication Timeline
.
Most widely held works by
Amie Wilkinson
Cocycles over partially hyperbolic maps by
Artur Avila(
Book
)
4 editions published in 2013 in English and held by 145 WorldCat member libraries worldwide
The works collected in this volume, while addressing quite different goals, are focused on the same type of mathematical object: cocycles over partially hyperbolic diffeomorphisms. We begin with a preliminary overview giving background on the history and applications of the study of dynamical cocycles and partially hyperbolic theory and elucidating the connections between the two main articles. The first one investigates effective conditions which ensure that the Lyapunov spectrum of a (possibly nonlinear) cocycle over a partially hyperbolic dynamical system is nontrivial. In the second one, the classical Livšic theory of the cohomological equation for Anosov diffeomorphisms is extended to accessible partially hyperbolic diffeomorphisms
4 editions published in 2013 in English and held by 145 WorldCat member libraries worldwide
The works collected in this volume, while addressing quite different goals, are focused on the same type of mathematical object: cocycles over partially hyperbolic diffeomorphisms. We begin with a preliminary overview giving background on the history and applications of the study of dynamical cocycles and partially hyperbolic theory and elucidating the connections between the two main articles. The first one investigates effective conditions which ensure that the Lyapunov spectrum of a (possibly nonlinear) cocycle over a partially hyperbolic dynamical system is nontrivial. In the second one, the classical Livšic theory of the cohomological equation for Anosov diffeomorphisms is extended to accessible partially hyperbolic diffeomorphisms
Dynamics done with your bare hands : lecture notes by Diana Davis, Bryce Weaver, Roland K.W. Roeder, Pablo Lessa by
Diana Davis(
Book
)
12 editions published in 2016 in English and Undetermined and held by 75 WorldCat member libraries worldwide
This book arose from 4 lectures given at the Undergraduate Summer School of the Thematic Program Dynamics and Boundaries held at the University of Notre Dame. It is intended to introduce (under)graduate students to the field of dynamical systems by emphasizing elementary examples, exercises and bare hands constructions. The lecture of Diana Davis is devoted to billiard flows on polygons, a simplesounding class of continuous time dynamical system for which many problems remain open. Bryce Weaver focuses on the dynamics of a 2x2 matrix acting on the flat torus. This example introduced by Vladimir Arnold illustrates the wide class of uniformly hyperbolic dynamical systems, including the geodesic flow for negatively curved, compact manifolds. Roland Roeder considers a dynamical system on the complex plane governed by a quadratic map with a complex parameter. These maps exhibit complicated dynamics related to the Mandelbrot set defined as the set of parameters for which the orbit remains bounded. Pablo Lessa deals with a type of nondeterministic dynamical system: a simple walk on an infinite graph, obtained by starting at a vertex and choosing a random neighbor at each step. The central question concerns the recurrence property. When the graph is a Cayley graph of a group, the behavior of the walk is deeply related to algebraic properties of the group
12 editions published in 2016 in English and Undetermined and held by 75 WorldCat member libraries worldwide
This book arose from 4 lectures given at the Undergraduate Summer School of the Thematic Program Dynamics and Boundaries held at the University of Notre Dame. It is intended to introduce (under)graduate students to the field of dynamical systems by emphasizing elementary examples, exercises and bare hands constructions. The lecture of Diana Davis is devoted to billiard flows on polygons, a simplesounding class of continuous time dynamical system for which many problems remain open. Bryce Weaver focuses on the dynamics of a 2x2 matrix acting on the flat torus. This example introduced by Vladimir Arnold illustrates the wide class of uniformly hyperbolic dynamical systems, including the geodesic flow for negatively curved, compact manifolds. Roland Roeder considers a dynamical system on the complex plane governed by a quadratic map with a complex parameter. These maps exhibit complicated dynamics related to the Mandelbrot set defined as the set of parameters for which the orbit remains bounded. Pablo Lessa deals with a type of nondeterministic dynamical system: a simple walk on an infinite graph, obtained by starting at a vertex and choosing a random neighbor at each step. The central question concerns the recurrence property. When the graph is a Cayley graph of a group, the behavior of the walk is deeply related to algebraic properties of the group
Stably ergodic approximation : two examples by
Michael Shub(
Book
)
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volumepreserving, partiallyhyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property."
3 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Abstract: "It has been conjectured that the stably ergodic diffeomorphisms are open and dense in the space of volumepreserving, partiallyhyperbolic diffeomorphisms of a compact manifold. In this paper we deal with two recalcitrant examples; the standard map cross Anosov and the ergodic automorphisms of the four torus. In both cases we show that they may be approximated by stably ergodic diffeomorphisms which have the stable accessibility property."
A stably Bernoullian diffeomorphism that is not Anosov by
Michael Shub(
Book
)
2 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
Stable ergodicity of the timeone map of a geodesic flow by
Amie Wilkinson(
)
3 editions published in 1995 in English and held by 6 WorldCat member libraries worldwide
Let M be a closed, connected Riemannian manifold with volume form $\omega$. A $C\sp2$, volumepreserving diffeomorphism $f:M\to M$ is stably ergodic if there is a neighborhood ${\cal U}$ of f in Diff$\sbsp{\omega}{2}(M)$, the space of $C\sp2$, volumepreserving diffeomorphisms of M, such that every $g\in{\cal U}$ is ergodic. Grayson, Pugh and Shub showed that if $\varphi\sb{t} : T\sb1S\to T\sb1S$ is the geodesic flow on the unit tangent bundle of a closed surface S of constant negative curvature, then the timeone map $\varphi\sb1$ is stably ergodic (Ann. of Math. 140, 1994). This is the first known example of a stably ergodic diffeomorphism that is not structurally stable. In this thesis, we extend this result to variable negative curvature. More precisely, our Main Theorem states: Main Theorem: If S is a closed, connected negativelycurved Riemannian surface, and if $\varphi\sb{t} : T\sb1S\to T\sb1S$ is the geodesic flow, then the timeone map $\varphi\sb1$ is stably ergodic
3 editions published in 1995 in English and held by 6 WorldCat member libraries worldwide
Let M be a closed, connected Riemannian manifold with volume form $\omega$. A $C\sp2$, volumepreserving diffeomorphism $f:M\to M$ is stably ergodic if there is a neighborhood ${\cal U}$ of f in Diff$\sbsp{\omega}{2}(M)$, the space of $C\sp2$, volumepreserving diffeomorphisms of M, such that every $g\in{\cal U}$ is ergodic. Grayson, Pugh and Shub showed that if $\varphi\sb{t} : T\sb1S\to T\sb1S$ is the geodesic flow on the unit tangent bundle of a closed surface S of constant negative curvature, then the timeone map $\varphi\sb1$ is stably ergodic (Ann. of Math. 140, 1994). This is the first known example of a stably ergodic diffeomorphism that is not structurally stable. In this thesis, we extend this result to variable negative curvature. More precisely, our Main Theorem states: Main Theorem: If S is a closed, connected negativelycurved Riemannian surface, and if $\varphi\sb{t} : T\sb1S\to T\sb1S$ is the geodesic flow, then the timeone map $\varphi\sb1$ is stably ergodic
Teichmüller curves in genus three and just likely intersections in Gnm x Gna by
Matt Bainbridge(
Book
)
2 editions published in 2016 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 2016 in English and held by 3 WorldCat member libraries worldwide
When an infinitelyrenormalizable endomorphism of the interval can be smoothed by Charles Tresser(
Book
)
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
Abstract: "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 of the ambient space M. We give a necessary condition for the smoothability of the faithfully infinitely intervalrenormalizable homeomorphisms of Cantor sets in the unit interval. This class contains, in particular, all minimal homeomorphisms of Cantor sets in the line which extend to continuous maps of an interval with zero topological entropy."
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
Abstract: "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 of the ambient space M. We give a necessary condition for the smoothability of the faithfully infinitely intervalrenormalizable homeomorphisms of Cantor sets in the unit interval. This class contains, in particular, all minimal homeomorphisms of Cantor sets in the line which extend to continuous maps of an interval with zero topological entropy."
Teichmueller curves in genus three and just likely intersections in G n/m x G n/a by
Matt Bainbridge(
Book
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
Three results on the regularity of the curves that are invariant by an exact symplectic twist map. Invariant subspaces for
operators in a general II 1factor[u.a.] / by Uffe Haagerup and Hanne Schultz. by
M.C Arnaud(
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
Prevalence of nonLipschitz Anosov foliations(
Book
)
2 editions published in 1997 in English and held by 0 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 0 WorldCat member libraries worldwide
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Avila, Artur 1979 Author
 Viana, Marcelo
 Santamaria, Jimmy
 Dal'boMilonet, Françoise Other Editor
 Ledrappier, F. Editor
 European Mathematical Society Publisher
 Lessa, Pablo (1982....). Other
 Davis, Diana Other Author
 Roeder, Roland K. W. (1978....). Other
 Weaver, Bryce Other
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Associated Subjects
Bernoulli shifts Cocycles Diffeomorphisms Differentiable dynamical systems Differential equations Dynamics Ergodic theory Geometry, Differential Group theory Manifolds (Mathematics) Morphisms (Mathematics) Number theory Random walks (Mathematics) Smoothing (Numerical analysis) Symmetric spaces University of California, Berkeley.Department of Mathematics
Alternative Names
Amie Wilkinson Amerikaans wiskundige
Amie Wilkinson amerikansk matematikar
Amie Wilkinson amerikansk matematiker
Amie Wilkinson matemática estadounidense
Amie Wilkinson Mathematician
Amie Wilkinson Mathématicienne américaine
Amie Wilkinson USamerikanische Mathematikerin
Wilkinson, A.
Wilkinson, Anne Marie.
امی ویلکینسن ریاضیدان آمریکایی
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