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Sunday, July 19, 2020 | History

9 edition of Dimension and recurrence in hyperbolic dynamics found in the catalog.

Dimension and recurrence in hyperbolic dynamics

by Luis Barreira

  • 128 Want to read
  • 28 Currently reading

Published by Birkhäuser, Springer, distributor] in Basel, [London .
Written in English

    Subjects:
  • Differentiable dynamical systems.,
  • Hyperbolic groups.,
  • Dimension theory (Topology)

  • Edition Notes

    Includes bibliographical references and index.

    StatementLuis Barreira.
    SeriesProgress in mathematics -- 272, Progress in mathematics (Boston, Mass.) -- v. 272.
    Classifications
    LC ClassificationsQA614.8 .B376 2008
    The Physical Object
    Paginationxiv, 300 p. :
    Number of Pages300
    ID Numbers
    Open LibraryOL22507589M
    ISBN 103764388811
    ISBN 109783764388812
    LC Control Number2008929876

    Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. This is definitely a soft question, but it was recently mentioned to me that one can study the dimension of fractals via ergodic methods. I'm familiar with ergodic theory on about the level of Einseidler and Ward, but googling for references is just bringing up papers that I can't follow or books that I don't have access to (without loaning from another library, but the semester is almost.

    Dimension theory in dynamical systems contemporary views and applications / by: Ergodic theory, hyperbolic dynamics and dimension theory by: Barreira, Luis, Published: () Dimension and recurrence in hyperbolic dynamics by: Barreira, Luis, Published. The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative shareholderdemocracy.com: Kindle.

    hyperbolic dynamics, dimension theory, and the thermodynamic for-malism are briefly recalled. We concentrate on uniformly hyperbolic dynamics, although we also refer to nonuniformly hyperbolic dynamics. Instead of always presenting the most general results, we made a selec-tion with the purpose of illustrating the main ideas while we avoid the. Lucarini, Faranda, Freitas, Freitas, Holland, Kuna, Nicol, Todd, Vaienti: Extremes and Recurrence in Dynamical Systems /5/16 page v v 11 Conclusions Main Concepts of This Book Extremes, Coarse Graining, and Parametrizations Extremes of Non-Autonomous Dynamical Systems


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Dimension and recurrence in hyperbolic dynamics by Luis Barreira Download PDF EPUB FB2

Dimension and Recurrence in Hyperbolic Dynamics (Progress in Mathematics Book ) - Kindle edition by Luis Barreira. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Dimension and Recurrence in Hyperbolic Dynamics (Progress in Mathematics Book ).

The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results. The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics.

It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative shareholderdemocracy.com by: The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics.

It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. This book offers a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics.

It examines the interplay of four main areas of. Dimension and Recurrence in Hyperbolic Dynamics by Luis Barreira,available Dimension and recurrence in hyperbolic dynamics book Book Depository with free delivery worldwide.

Dimension and recurrence in hyperbolic dynamics. 1 Contents of the book: a brief tour 3 2 Basic Notions 7 Dimension theory 7 Ergodic theory 13 Thermodynamic formalism 14 I Dimension Theory 17 3 Dimension Theory and Thermodynamic Formalism 19 Dimension theory of.

Dimension and Recurrence in Hyperbolic Dynamics. Dimension and Recurrence in Cite as. Pointwise Dimension for Hyperbolic Dynamics. Chapter. Downloads; Part of the Progress in Mathematics book series Pointwise Dimension for Hyperbolic Dynamics. In: Dimension and Recurrence in Hyperbolic Dynamics.

Progress in Mathematics, vol The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative.

Home» MAA Publications» MAA Reviews» Dimension and Recurrence in Hyperbolic Dynamics. Dimension and Recurrence in Hyperbolic Dynamics. Luis Barreira. Publisher: Birkhäuser.

Publication Date: Number of Pages: Category: Monograph. MAA Review; Table of Contents; We do not plan to review this book. Dimension Spectra of Hyperbolic Flows. book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the.

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This site is like a library, Use search box in. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics.

I hope that the book may serve as a fast entry point to this exciting and active?eld of research, and also that. INTRODUCTION TO PARTIALLY HYPERBOLIC DYNAMICS.

7 On surface, any hyperbolic chain-recurrence class is described by one of the examples of section The general classification of Anosov systems or of higher-dimensional hyperbolicchain-recurrence class isstillunknown.

Partially hyperbolic dynamics. Reduction of the dimension and normally hyperbolic manifolds 47 Equivalently, a diffeomorphism is hyperbolic if each of its chain-recurrence classes is a hyperbolic set. Example 1: the whole manifold. INTRODUCTION TO PARTIALLY HYPERBOLIC DYNAMICS 7 d.

Classification. A complement: Another question, which turned out to be much more difficult, is whether Poincaré recurrence can be quantified, that is, whether one can say something about the speed with which the orbits recur to a given set of positive measure.

For details about this, I recommend Barreira's book Dimension and Recurrence in Hyperbolic Dynamics. Is entropy related to Poincare recurrence time. Ask Question Asked 5 years, 2 months I recommend the book "Dimension and Recurrence in Hyperbolic Dynamics", by Barreira.

share The terms (not the results) in my answer are really at the rudiments of dynamics (which is the canonical area of Poincaré recurrence).

Because of this, my view. The dynamics of f on a hyperbolic set, or hyperbolic dynamics, exhibits features of local structural stability and has been much studied, cf. Axiom A. Definition.

Let M be a compact smooth manifold, f: M → M a diffeomorphism, and Df: TM → TM the differential of f. One of the ideas involved in the concept of entropy is that nature tends from order to disorder in isolated systems. But we even know that Poincare recurrence time also is a particular time after which a system of particles get back to their original position,and entropy is how can a system of particles be arranged.

So are these two related. For an average conformal hyperbolic set of a $ C^1 $ diffeomorphism, utilizing the techniques in sub-additive thermodynamic formalism and some geometric arguments with unstable/stable manifolds, a formula of the Hausdorff dimension and lower (upper) box dimension is given in this paper, which is exactly the sum of the dimensions of the Author: Juan Wang, Jing Wang, Yongluo Cao, Yun Zhao.

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean shareholderdemocracy.com parallel postulate of Euclidean geometry is replaced with.

For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R.hyperbolic dynamics, dimension theory, and the thermodynamic for-malism are brie Key words and phrases.

dimension, hyperbolicity, recurrence. Partially supported by the Center for Mathematical Analysis, Geometry, and Dynam- reference that clearly took this point of view is the book .springer, The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research.

Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors.