Structure Of Dynamical Systems

Author : J.M. Souriau
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202813

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Structure of Dynamical Systems by J.M. Souriau Pdf

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 : Jean-Marie Souriau
Publisher : Unknown
Page : 406 pages
File Size : 41,7 Mb
Release : 1997
Category : Electronic
ISBN : 3764336951

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Structure of Dynamical Systems (Structure Des Systemes Dynamiques) by Jean-Marie Souriau Pdf

Author : J.M. Souriau
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 51,8 Mb
Release : 1997-09-23
Category : Mathematics
ISBN : 0817636951

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Structure of Dynamical Systems by J.M. Souriau Pdf

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 : Philip Holmes
Publisher : Cambridge University Press
Page : 403 pages
File Size : 47,7 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9781107008250

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Turbulence, Coherent Structures, Dynamical Systems and Symmetry by Philip Holmes Pdf

Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.

Author : George Osipenko
Publisher : Springer
Page : 286 pages
File Size : 51,5 Mb
Release : 2006-10-28
Category : Mathematics
ISBN : 9783540355953

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Dynamical Systems, Graphs, and Algorithms by George Osipenko Pdf

This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

Author : Marcel de Jeu
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 52,8 Mb
Release : 2009-11-30
Category : Mathematics
ISBN : 9780821847473

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Operator Structures and Dynamical Systems by Marcel de Jeu Pdf

This volume contains the proceedings of a Leiden Workshop on Dynamical Systems and their accompanying Operator Structures which took place at the Lorentz Center in Leiden, The Netherlands, on July 21-25, 2008. These papers offer a panorama of selfadjoint and non-selfadjoint operator algebras associated with both noncommutative and commutative (topological) dynamical systems and related subjects. Papers on general theory, as well as more specialized ones on symbolic dynamics and complex dynamical systems, are included.

Author : Arjan J. van der Schaft,Hans Schumacher
Publisher : Springer
Page : 189 pages
File Size : 54,9 Mb
Release : 2007-10-03
Category : Technology & Engineering
ISBN : 9781846285424

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An Introduction to Hybrid Dynamical Systems by Arjan J. van der Schaft,Hans Schumacher Pdf

This book is about dynamical systems that are "hybrid" in the sense that they contain both continuous and discrete state variables. Recently there has been increased research interest in the study of the interaction between discrete and continuous dynamics. The present volume provides a first attempt in book form to bring together concepts and methods dealing with hybrid systems from various areas, and to look at these from a unified perspective. The authors have chosen a mode of exposition that is largely based on illustrative examples rather than on the abstract theorem-proof format because the systematic study of hybrid systems is still in its infancy. The examples are taken from many different application areas, ranging from power converters to communication protocols and from chaos to mathematical finance. Subjects covered include the following: definition of hybrid systems; description formats; existence and uniqueness of solutions; special subclasses (variable-structure systems, complementarity systems); reachability and verification; stability and stabilizability; control design methods. The book will be of interest to scientists from a wide range of disciplines including: computer science, control theory, dynamical system theory, systems modeling and simulation, and operations research.

Author : Henning Mortveit,Christian Reidys
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 49,6 Mb
Release : 2007-11-27
Category : Mathematics
ISBN : 9780387498799

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An Introduction to Sequential Dynamical Systems by Henning Mortveit,Christian Reidys Pdf

This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.

Author : Eduard Zehnder
Publisher : European Mathematical Society
Page : 372 pages
File Size : 54,5 Mb
Release : 2010
Category : Dynamics
ISBN : 3037190817

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Lectures on Dynamical Systems by Eduard Zehnder Pdf

This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 46,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662067918

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Dynamical Systems IV by V.I. Arnol'd,S.P. Novikov Pdf

From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992

Author : S.P. Novikov
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 52,9 Mb
Release : 2001-06-20
Category : Mathematics
ISBN : 3540626352

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Dynamical Systems IV by S.P. Novikov Pdf

From the reviews of the first edition:"... Here ... a wealth of material is displayed for us, too much to even indicate in a review. ... Your reviewer was very impressed by the contents of both volumes (EMS 2 and 4), recommending them without any restriction." Mededelingen van het Wiskundig genootshap 1992

Author : Luis Barreira,Claudia Valls
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 50,5 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9781447148357

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Dynamical Systems by Luis Barreira,Claudia Valls Pdf

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem. The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology. This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.

Author : Peter L. Christiansen,Robert D. Parmentier
Publisher : Manchester University Press
Page : 702 pages
File Size : 48,6 Mb
Release : 1989
Category : Chaotic behavior in systems
ISBN : 0719026105

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Structure, Coherence and Chaos in Dynamical Systems by Peter L. Christiansen,Robert D. Parmentier Pdf

Author : V.I. Arnol'd,S.P. Novikov
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 47,9 Mb
Release : 1993-12-06
Category : Mathematics
ISBN : 3540181768

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Dynamical Systems VII by V.I. Arnol'd,S.P. Novikov Pdf

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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,7 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9789814462716

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Nonlinear Dynamical Systems of Mathematical Physics by Anonim Pdf