On Random Perturbations Of Hamiltonian Systems With Many Degrees Of Freedom
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Random Perturbations Of Dynamical Systems
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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-31
Random Perturbations Of Dynamical Systems written by Mark I. Freidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-31 with Mathematics categories.
Many notions and results presented in the previous editions of this volume have since become quite popular in applications, and many of them have been “rediscovered” in applied papers. In the present 3rd edition small changes were made to the chapters in which long-time behavior of the perturbed system is determined by large deviations. Most of these changes concern terminology. In particular, it is explained that the notion of sub-limiting distribution for a given initial point and a time scale is identical to the idea of metastability, that the stochastic resonance is a manifestation of metastability, and that the theory of this effect is a part of the large deviation theory. The reader will also find new comments on the notion of quasi-potential that the authors introduced more than forty years ago, and new references to recent papers in which the proofs of some conjectures included in previous editions have been obtained. Apart from the above mentioned changes the main innovations in the 3rd edition concern the averaging principle. A new Section on deterministic perturbations of one-degree-of-freedom systems was added in Chapter 8. It is shown there that pure deterministic perturbations of an oscillator may lead to a stochastic, in a certain sense, long-time behavior of the system, if the corresponding Hamiltonian has saddle points. The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section. Also a new Chapter 9 has been inserted in which deterministic and stochastic perturbations of systems with many degrees of freedom are considered. Because of the resonances, stochastic regularization in this case is even more important.
On Random Perturbations Of Hamiltonian Systems With Many Degrees Of Freedom
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Author : Mark I. Frejdlin
language : en
Publisher:
Release Date : 2000
On Random Perturbations Of Hamiltonian Systems With Many Degrees Of Freedom written by Mark I. Frejdlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Topics In Stochastic Analysis And Nonparametric Estimation
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Author : Pao-Liu Chow
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-19
Topics In Stochastic Analysis And Nonparametric Estimation written by Pao-Liu Chow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-19 with Mathematics categories.
This IMA Volume in Mathematics and its Applications TOPICS IN STOCHASTIC ANALYSIS AND NONPARAMETRIC ESTIMATION contains papers that were presented at the IMA Participating Institution conference on "Asymptotic Analysis in Stochastic Processes, Nonparamet ric Estimation, and Related Problems" held on September 15-17, 2006 at Wayne State University. The conference, which was one of approximately ten selected each year for partial support by the IMA through its affiliates program, was dedicated to Professor Rafail Z. Khasminskii on the occasion th of his 75 birthday, in recognition of his profound contributions to the field of stochastic processes and nonparametric estimation theory. We are grateful to the participants and, especially, to the conference organizers, for making the event so successful. Pao-Liu Chow, Boris Mor dukhovich, and George Yin of the Department of Mathematics at Wayne State University did a superb job organizing this first-rate event and in editing these proceedings. We take this opportunity to thank the Nation al Science Foundation for its support of the IMA.
Hamiltonian Dynamical Systems
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Author : R.S MacKay
language : en
Publisher: CRC Press
Release Date : 2020-08-18
Hamiltonian Dynamical Systems written by R.S MacKay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.
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.
Games Of No Chance 3
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Author : Michael H. Albert
language : en
Publisher: Cambridge University Press
Release Date : 2009-05-29
Games Of No Chance 3 written by Michael H. Albert and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-29 with Mathematics categories.
This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyses of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles. The volume is rounded out with an up-to-date bibliography by Fraenkel and, for readers eager to get their hands dirty, a list of unsolved problems by Guy and Nowakowski. Highlights include some of Siegel's groundbreaking work on loopy games, the unveiling by Friedman and Landsberg of the use of renormalization to give very intriguing results about Chomp, and Nakamura's "Counting Liberties in Capturing Races of Go." Like its predecessors, this book should be on the shelf of all serious games enthusiasts.
Random Perturbations Of Dynamical Systems
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Author : M. I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Perturbations Of Dynamical Systems written by M. I. Freidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Asymptotical problems have always played an important role in probability theory. In classical probability theory dealing mainly with sequences of independent variables, theorems of the type of laws of large numbers, theorems of the type of the central limit theorem, and theorems on large deviations constitute a major part of all investigations. In recent years, when random processes have become the main subject of study, asymptotic investigations have continued to playa major role. We can say that in the theory of random processes such investigations play an even greater role than in classical probability theory, because it is apparently impossible to obtain simple exact formulas in problems connected with large classes of random processes. Asymptotical investigations in the theory of random processes include results of the types of both the laws of large numbers and the central limit theorem and, in the past decade, theorems on large deviations. Of course, all these problems have acquired new aspects and new interpretations in the theory of random processes.
Hamiltonian Dynamical Systems And Applications
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Author : Walter Craig
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Hamiltonian Dynamical Systems And Applications written by Walter Craig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-17 with Mathematics categories.
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Turbulence And Self Organization
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Author : Mikhail Ya Marov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-16
Turbulence And Self Organization written by Mikhail Ya Marov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-16 with Science categories.
The book deals with the development of continual models of turbulent natural media. Such models serve as a ground for the statement and numerical evaluation of the key problems of the structure and evolution of the numerous astrophysical and geophysical objects. The processes of ordering (self-organization) in an originally chaotic turbulent medium are addressed and treated in detail with the use of irreversible thermodynamics and stochastic dynamics approaches which underlie the respective models. Different examples of ordering set up in the natural environment and outer space are brought and thoroughly discussed, the main focus being given to the protoplanetary discs formation and evolution.
Coherent Dynamics Of Complex Quantum Systems
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Author : Vladimir M. Akulin
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-09-13
Coherent Dynamics Of Complex Quantum Systems written by Vladimir M. Akulin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-13 with Science categories.
Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.
Nonlinearity
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Author :
language : en
Publisher:
Release Date : 2009-10
Nonlinearity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10 with Mathematical analysis categories.