Author : Anatole Katok
Publisher : Springer
Page : 292 pages
File Size : 47,27 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540473491
Author : Anatole Katok
Publisher :
Page : 300 pages
File Size : 30,31 MB
Release : 2014-01-15
Category :
ISBN : 9783662175422
Author :
Publisher :
Page : 283 pages
File Size : 25,83 MB
Release : 1964
Category : Differentiable dynamical systems
ISBN : 9780387171906
Author : Joel E. Cohen
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 20,9 MB
Release : 1986
Category : Mathematics
ISBN : 082185044X
Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.
Author : Cesar E. Silva
Publisher : Springer Nature
Page : 707 pages
File Size : 11,55 MB
Release : 2023-07-31
Category : Mathematics
ISBN : 1071623885
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
Author : Rafael Labarca
Publisher : CRC Press
Page : 460 pages
File Size : 13,82 MB
Release : 1993-02-22
Category : Mathematics
ISBN : 9780582216211
In at least five countries in Latin America, high level research in the field in taking place. To stimulate this development both at home and abroad, Chilean mathematicians have been promoting international meetings like the III International School of Dynamical Systems, which took place at the Universidad de Santiago de Chile-Santiago in 1990. A number of distinguished mathematicians were present at the meeting, side by side with younger people interested in the subject. Several of the participants submitted original contributions to these proceedings of the school. The topics of the papers are central to dynamics: ergodic theory, real and complex foliations, fractal dimensions, polynomial vector fields, hyperbolicity, and expansive maps. Notes on the ergodic theory of plane billiards are also included. This book will be of particular interest to researchers and graduate students working in mathematics, particularly in ordinary differential equations, bifurcation theory, and dynamical systems. Also those working in mathematical physics and physics.
Author : Vesselin M. Petkov
Publisher : John Wiley & Sons
Page : 428 pages
File Size : 26,45 MB
Release : 2017-01-30
Category : Mathematics
ISBN : 1119107660
This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents these in a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory. The content of the first edition is still relevant, however the new edition will include several new results established after 1992; new text will comprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques which will be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.
Author : Manfred Einsiedler
Publisher : Springer Nature
Page : 232 pages
File Size : 34,30 MB
Release :
Category :
ISBN : 3031620143
Author : Boris Hasselblatt
Publisher : Springer
Page : 334 pages
File Size : 22,15 MB
Release : 2017-12-15
Category : Mathematics
ISBN : 3319430599
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
Page : 458 pages
File Size : 29,86 MB
Release : 2013-12-11
Category : Mathematics
ISBN : 366204062X
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.
