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Author: J.M. Souriau
Publisher: Springer Science & Business Media
ISBN: 1461202817
Category : Mathematics
Languages : en
Pages : 427
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Book Description
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
Author: J.M. Souriau
Publisher: Springer Science & Business Media
ISBN: 1461202817
Category : Mathematics
Languages : en
Pages : 427
Get Book Here
Book Description
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
Author: Kotik K. Lee
Publisher: World Scientific
ISBN: 9789971509651
Category : Science
Languages : en
Pages : 476
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Book Description
The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Author: Peter L. Christiansen
Publisher: Manchester University Press
ISBN: 9780719026102
Category : Chaotic behavior in systems
Languages : en
Pages : 702
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Book Description
Author: Jared Maruskin
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110597802
Category : Science
Languages : en
Pages : 350
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Book Description
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
ISBN: 366206796X
Category : Mathematics
Languages : en
Pages : 346
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Book Description
A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 1461415233
Category : Mathematics
Languages : en
Pages : 500
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Book Description
Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.
Author: Michael Brin
Publisher: Cambridge University Press
ISBN: 9780521840736
Category : Mathematics
Languages : en
Pages : 490
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Book Description
This volume presents a broad collection of current research by leading experts in the theory of dynamical systems.
Author: H.W. Broer
Publisher: Elsevier
ISBN: 0444596259
Category : Science
Languages : en
Pages : 323
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Book Description
The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account.Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs.All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
Author: E. W. C. van Groesen
Publisher: North Holland
ISBN:
Category : Mathematics
Languages : en
Pages : 644
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Book Description
This work addresses several aspects of continuous dynamical systems, all of which can be viewed as generalizations of methods from classical mechnics. Equations such as the Korteweg-de Vries, non-linear Schrodinger, Sine-Gordon and Boussinesq equations are treated in detail.
Author: Sergei Yu. Pilyugin
Publisher: Walter de Gruyter
ISBN: 3110258412
Category : Science
Languages : en
Pages : 244
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Book Description
Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion. In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories are covered, as well as nonlinearity. The author is an experienced book writer and his work is based on years of teaching.
