Ergodic Theory Of Equivariant Diffeomorphisms

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Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity

Author : Mike Field
Publisher : American Mathematical Soc.
ISBN 13 : 0821835998
Total Pages : 113 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity by : Mike Field

Download or read book Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity written by Mike Field and published by American Mathematical Soc.. This book was released on 2004 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).

Ergodic Theory of Equivariant Diffeomorphisms

Author : Mike Field
Publisher : American Mathematical Soc.
ISBN 13 : 9781470404017
Total Pages : 100 pages
Book Rating : 4.4/5 (4 download)

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Book Synopsis Ergodic Theory of Equivariant Diffeomorphisms by : Mike Field

Download or read book Ergodic Theory of Equivariant Diffeomorphisms written by Mike Field and published by American Mathematical Soc.. This book was released on 2004 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: We obtain stability and structural results for equivariant diffeomorphisms which are hyperbolic transverse to a compact (connected or finite) Lie group action and construct '$\Gamma$-regular' Markov partitions which give symbolic dynamics on the orbit space. We apply these results to the situation where $\Gamma$ is a compact connected Lie group acting smoothly on $M$ and $F$ is a smooth (at least $C^2$) $\Gamma$-equivariant diffeomorphism of $M$ such that the restriction of $F$ to the $\Gamma$- and $F$-invariant set $\Lambda\subset M$ is partially hyperbolic with center foliation given by $\Gamma$-orbits.On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, we show that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free). In this setting we prove a version of the Livsic regularity theorem and extend results of Brin on the structure of the ergodic components of compact group extensions of Anosov diffeomorphisms. We show as our main result that generically $(F,\Lambda,\nu)$ is stably ergodic (openness in the $C^2$-topology). In the case when $\Lambda$ is an attractor, we show that $\Lambda$ is generically a stably SRB attractor within the class of $\Gamma$-equivariant diffeomorphisms of $M$.

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

Author : Rufus Bowen
Publisher : Springer
ISBN 13 : 3540375341
Total Pages : 114 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms by : Rufus Bowen

Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by Rufus Bowen and published by Springer. This book was released on 2006-11-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface by D. Ruelle:“...Rufus Bowen has left us a masterpiece of mathematical exposition... Here a numberof results which were new at the time are presented in such a clear and lucid style thatBowen's monograph immediately became a classic. More than thirty years later, manynew results have been proved in this area, but the volume is as useful as ever because itremains the best introduction to the basics of the ergodic theory of hyperbolic systems.’’ For this printing of R. Bowen’s book, J.-R. Chazottes has rekeyed it in TeX for easierreading, thereby correcting typos and bibliographic details.

Ergodic Theory

Author : Cesar E. Silva
Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Bifurcation, Symmetry and Patterns

Author : Jorge Buescu
Publisher : Birkhäuser
ISBN 13 : 3034879822
Total Pages : 215 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Bifurcation, Symmetry and Patterns by : Jorge Buescu

Download or read book Bifurcation, Symmetry and Patterns written by Jorge Buescu and published by Birkhäuser. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest developments on both the theory and applications of bifurcations with symmetry. The text includes recent experimental work as well as new approaches to and applications of the theory to other sciences. It shows the range of dissemination of the work of Martin Golubitsky and Ian Stewart and its influence in modern mathematics at the same time as it contains work of young mathematicians in new directions. The range of topics includes mathematical biology, pattern formation, ergodic theory, normal forms, one-dimensional dynamics and symmetric dynamics.

Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result

Author : Valentin Poenaru
Publisher : American Mathematical Soc.
ISBN 13 : 0821834606
Total Pages : 104 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result by : Valentin Poenaru

Download or read book Equivariant, Almost-Arborescent Representations of Open Simply-Connected 3-Manifolds; A Finiteness Result written by Valentin Poenaru and published by American Mathematical Soc.. This book was released on 2004 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows that at the cost of replacing $V DEGREES3$ by $V_h DEGREES3 = \{V DEGREES3$ with very many holes $\}$, we can always find representations $X DEGREES2 \stackrel {f} {\rightarrow} V DEGREES3$ with $X DEGREES2$ locally finite and almost-arborescent, with $\Psi (f)=\Phi (f)$, and with the ope

Dynamics, Ergodic Theory and Geometry

Author : Boris Hasselblatt
Publisher : Cambridge University Press
ISBN 13 : 0521875412
Total Pages : 324 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Dynamics, Ergodic Theory and Geometry by : Boris Hasselblatt

Download or read book Dynamics, Ergodic Theory and Geometry written by Boris Hasselblatt and published by Cambridge University Press. This book was released on 2007-09-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

Dynamics And Symmetry

Author : Michael Field
Publisher : World Scientific
ISBN 13 : 1908979178
Total Pages : 493 pages
Book Rating : 4.9/5 (89 download)

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Book Synopsis Dynamics And Symmetry by : Michael Field

Download or read book Dynamics And Symmetry written by Michael Field and published by World Scientific. This book was released on 2007-09-03 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems.This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone./a

The Complex Monge-Ampere Equation and Pluripotential Theory

Author : Sławomir Kołodziej
Publisher : American Mathematical Soc.
ISBN 13 : 082183763X
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Complex Monge-Ampere Equation and Pluripotential Theory by : Sławomir Kołodziej

Download or read book The Complex Monge-Ampere Equation and Pluripotential Theory written by Sławomir Kołodziej and published by American Mathematical Soc.. This book was released on 2005 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.

Dynamical Properties of Diffeomorphisms of the Annulus and of the Torus

Author : Patrice Le Calvez
Publisher : American Mathematical Soc.
ISBN 13 : 9780821819432
Total Pages : 124 pages
Book Rating : 4.8/5 (194 download)

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Book Synopsis Dynamical Properties of Diffeomorphisms of the Annulus and of the Torus by : Patrice Le Calvez

Download or read book Dynamical Properties of Diffeomorphisms of the Annulus and of the Torus written by Patrice Le Calvez and published by American Mathematical Soc.. This book was released on 2000 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The second chapter generalizes some aspects of Aubry-Mather theory to such maps and presents a version of the Poincare-Birkhoff theorem in which the periodic orbits have the same braid type as in the linear case. A diffeomorphism of the torus isotopic to the identity is also a composition of twist maps, and it is possible to obtain a proof of the Conley-Zehnder theorem with the same kind of conclusions about the braid type, in the case of periodic orbits. This results leads to an equivariant version of the Brouwer translation theorem which permits new proofs of some results about the rotation set of diffeomorphisms of the torus."--BOOK JACKET.

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations

Author : Greg Hjorth
Publisher : American Mathematical Soc.
ISBN 13 : 0821837710
Total Pages : 126 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations by : Greg Hjorth

Download or read book Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2005 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.

Quasi-Ordinary Power Series and Their Zeta Functions

Author : Enrique Artal-Bartolo
Publisher : American Mathematical Soc.
ISBN 13 : 9780821865637
Total Pages : 100 pages
Book Rating : 4.8/5 (656 download)

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Book Synopsis Quasi-Ordinary Power Series and Their Zeta Functions by : Enrique Artal-Bartolo

Download or read book Quasi-Ordinary Power Series and Their Zeta Functions written by Enrique Artal-Bartolo and published by American Mathematical Soc.. This book was released on 2005-10-05 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h,T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h,T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex $R\psi_h$ of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.

Uniformizing Dessins and BelyiMaps via Circle Packing

Author : Philip L. Bowers
Publisher : American Mathematical Soc.
ISBN 13 : 0821835238
Total Pages : 118 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Uniformizing Dessins and BelyiMaps via Circle Packing by : Philip L. Bowers

Download or read book Uniformizing Dessins and BelyiMaps via Circle Packing written by Philip L. Bowers and published by American Mathematical Soc.. This book was released on 2004 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.

A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring

Author : Ehud Friedgut
Publisher : American Mathematical Soc.
ISBN 13 : 0821838253
Total Pages : 80 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring by : Ehud Friedgut

Download or read book A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring written by Ehud Friedgut and published by American Mathematical Soc.. This book was released on 2006 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper the authors establish a sharp threshold for random graphs with this property. Let $G(n, p)$ be the random graph on $n$ vertices with edge probability $p$. The authors prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\left[G(n, (1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right] \rightarrow 0$ and $Pr \left[ G(n, (1]\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right] \rightarrow 1.$. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setti

Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines

Author : Hagen Meltzer
Publisher : American Mathematical Soc.
ISBN 13 : 082183519X
Total Pages : 154 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines by : Hagen Meltzer

Download or read book Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines written by Hagen Meltzer and published by American Mathematical Soc.. This book was released on 2004 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves.

Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis

Author : J. T. Cox
Publisher : American Mathematical Soc.
ISBN 13 : 0821835424
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis by : J. T. Cox

Download or read book Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis written by J. T. Cox and published by American Mathematical Soc.. This book was released on 2004 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.

Kahler Spaces, Nilpotent Orbits, and Singular Reduction

Author : Johannes Huebschmann
Publisher : American Mathematical Soc.
ISBN 13 : 0821835726
Total Pages : 110 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Kahler Spaces, Nilpotent Orbits, and Singular Reduction by : Johannes Huebschmann

Download or read book Kahler Spaces, Nilpotent Orbits, and Singular Reduction written by Johannes Huebschmann and published by American Mathematical Soc.. This book was released on 2004 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.