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Author : Luis Barreira
Release : 1995
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis A Non-additive Thermodynamic Formalism and Applications to the Dimension Theory of Hyperbolic Dynamics by : Luis Barreira
Download or read book A Non-additive Thermodynamic Formalism and Applications to the Dimension Theory of Hyperbolic Dynamics written by Luis Barreira. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Luis Barreira
Release : 2011-08-24
Genre : Mathematics
Kind : eBook
Book Rating : 064/5 ( reviews)
Book Synopsis Thermodynamic Formalism and Applications to Dimension Theory by : Luis Barreira
Download or read book Thermodynamic Formalism and Applications to Dimension Theory written by Luis Barreira. This book was released on 2011-08-24. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.
Author : Luís Barreira
Release : 2012-04-28
Genre : Mathematics
Kind : eBook
Book Rating : 900/5 ( reviews)
Book Synopsis Ergodic Theory, Hyperbolic Dynamics and Dimension Theory by : Luís Barreira
Download or read book Ergodic Theory, Hyperbolic Dynamics and Dimension Theory written by Luís Barreira. This book was released on 2012-04-28. Available in PDF, EPUB and Kindle. Book excerpt: 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. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.
Author : Luís Barreira
Release : 2013-06-12
Genre : Mathematics
Kind : eBook
Book Rating : 480/5 ( reviews)
Book Synopsis Dimension Theory of Hyperbolic Flows by : Luís Barreira
Download or read book Dimension Theory of Hyperbolic Flows written by Luís Barreira. This book was released on 2013-06-12. Available in PDF, EPUB and Kindle. Book excerpt: 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. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs. The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.
Author : Mark Pollicott
Release : 2021-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 634/5 ( reviews)
Book Synopsis Thermodynamic Formalism by : Mark Pollicott
Download or read book Thermodynamic Formalism written by Mark Pollicott. This book was released on 2021-10-01. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
