Invariant Manifolds, Entropy and Billiards. Smooth Maps with Singularities PDF Download

Author: Anatole Katok
Publisher: Springer
ISBN: 3540473491
Category : Mathematics
Languages : en
Pages : 292

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Author: Anatole Katok
Publisher:
ISBN: 9783662175422
Category :
Languages : en
Pages : 300

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Author:
Publisher:
ISBN: 9780387171906
Category : Differentiable dynamical systems
Languages : en
Pages : 283

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Author: A. B. Katok
Publisher:
ISBN:
Category :
Languages : en
Pages : 306

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Author: Boris Hasselblatt
Publisher: Springer
ISBN: 3319430599
Category : Mathematics
Languages : en
Pages : 334

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Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.

Author: D. Szasz
Publisher: Springer Science & Business Media
ISBN: 366204062X
Category : Mathematics
Languages : en
Pages : 458

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Hard Ball Systems and the Lorentz Gas are fundamental models arising in the theory of Hamiltonian dynamical systems. Moreover, in these models, some key laws of statistical physics can also be tested or even established by mathematically rigorous tools. The mathematical methods are most beautiful but sometimes quite involved. This collection of surveys written by leading researchers of the fields - mathematicians, physicists or mathematical physicists - treat both mathematically rigourous results, and evolving physical theories where the methods are analytic or computational. Some basic topics: hyperbolicity and ergodicity, correlation decay, Lyapunov exponents, Kolmogorov-Sinai entropy, entropy production, irreversibility. This collection is a unique introduction into the subject for graduate students, postdocs or researchers - in both mathematics and physics - who want to start working in the field.

Author: Morris W. Hirsch
Publisher: Springer Science & Business Media
ISBN: 1461227402
Category : Mathematics
Languages : en
Pages : 620

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An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati cians working in the many fields to which Smale has made lasting con tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.

Author: Y. Takahashi
Publisher: Springer Science & Business Media
ISBN: 1461303214
Category : Mathematics
Languages : en
Pages : 222

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In 1992 two successive symposia were held in Japan on algorithms, fractals and dynamical systems. The first one was Hayashibara Forum '92: International Symposium on New Bases for Engineering Science, Algorithms, Dynamics and Fractals held at Fujisaki Institute of Hayashibara Biochemical Laboratories, Inc. in Okayama during November 23-28 in which 49 mathematicians including 19 from abroad participated. They include both pure and applied mathematicians of diversified backgrounds and represented 11 coun tries. The organizing committee consisted of the following domestic members and Mike KEANE from Delft: Masayosi HATA, Shunji ITO, Yuji ITO, Teturo KAMAE (chairman), Hitoshi NAKADA, Satoshi TAKAHASHI, Yoichiro TAKAHASHI, Masaya YAMAGUTI The second one was held at the Research Institute for Mathematical Science at Kyoto University from November 30 to December 2 with emphasis on pure mathematical side in which more than 80 mathematicians participated. This volume is a partial record of the stimulating exchange of ideas and discussions which took place in these two symposia.

Author: R.S MacKay
Publisher: CRC Press
ISBN: 1000156893
Category : Mathematics
Languages : en
Pages : 808

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Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

Author: G Gyorgyi
Publisher: World Scientific
ISBN: 981450565X
Category : Science
Languages : en
Pages : 602

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Book Description
This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Péter Szépfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.