Classical Dynamical Systems

Author : Valeriĭ Viktorovich Kozlov
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 43,6 Mb
Release : 1995
Category : Mathematics
ISBN : 0821804278

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Dynamical Systems in Classical Mechanics by Valeriĭ Viktorovich Kozlov Pdf

This book shows that the phenomenon of integrability is related not only to Hamiltonian systems, but also to a wider variety of systems having invariant measures that often arise in nonholonomic mechanics. Each paper presents unique ideas and original approaches to various mathematical problems related to integrability, stability, and chaos in classical dynamics. Topics include... the inverse Lyapunov theorem on stability of equilibria geometrical aspects of Hamiltonian mechanics from a hydrodynamic perspective current unsolved problems in the dynamical systems approach to classical mechanics.

Author : Walter Thirring
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 42,5 Mb
Release : 2003-10-17
Category : Science
ISBN : 0387406158

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Classical Mathematical Physics by Walter Thirring Pdf

This volume combines the enlarged and corrected editions of both volumes on classical physics of Thirring's famous course in mathematical physics. With numerous examples and remarks accompanying the text, it is suitable as a textbook for students in physics, mathematics, and applied mathematics. The treatment of classical dynamical systems uses analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems, canonical transformations, constants of motion, and pertubation theory. Problems discussed in considerable detail include: nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses the language of differenial geometry throughout, treating both Maxwell's and Einstein's equations in a compact and clear fashion. The book includes discussions of the electromagnetic field due to known charge distributions and in the presence of conductors as well as a new section on gauge theories. It discusses the solutions of the Einstein equations for maximally symmetric spaces and spaces with maximally symmetric submanifolds; it concludes by applying these results to the life and death of stars.

Author : Walter Thirring,Evans M. Harrell
Publisher : Springer
Page : 271 pages
File Size : 53,8 Mb
Release : 2013-12-01
Category : Science
ISBN : 9783662398920

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Classical Dynamical Systems by Walter Thirring,Evans M. Harrell Pdf

Author : Yirong Liu,Jibin Li,Wentao Huang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 464 pages
File Size : 54,8 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110389142

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Planar Dynamical Systems by Yirong Liu,Jibin Li,Wentao Huang Pdf

In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.

Author : Walter E. Thirring
Publisher : Unknown
Page : 257 pages
File Size : 49,9 Mb
Release : 1978
Category : Electronic
ISBN : OCLC:488792456

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A course in mathematical physics. 1 by Walter E. Thirring Pdf

Author : Walter Thirring
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468405170

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A Course in Mathematical Physics 1 and 2 by Walter Thirring Pdf

The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap ter with the proof of the K-A-M Theorem to make allowances for the cur rent trend in physics. This involved not only the use of more refined mathe matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the planetary orbits, and which used to be passed over in silence as mystical nonsense, seem to point the way to a truth unattainable by superficial observation: The ratios of the radii of Platonic solids to the radii of inscribed Platonic solids are irrational, but satisfy algebraic equations of lower order.

Author : Walter Thirring
Publisher : Springer
Page : 0 pages
File Size : 53,9 Mb
Release : 2012
Category : Mathematics
ISBN : 1468494309

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A Course in Mathematical Physics 1 by Walter Thirring Pdf

Author : Kenneth R. Meyer,Daniel C. Offin
Publisher : Springer
Page : 384 pages
File Size : 48,5 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9783319536910

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth R. Meyer,Daniel C. Offin Pdf

This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)

Author : Aidan Sims,Gábor Szabó,Dana Williams
Publisher : Springer Nature
Page : 163 pages
File Size : 46,9 Mb
Release : 2020-06-22
Category : Mathematics
ISBN : 9783030397135

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Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension by Aidan Sims,Gábor Szabó,Dana Williams Pdf

This book collects the notes of the lectures given at the Advanced Course on Crossed Products, Groupoids, and Rokhlin dimension, that took place at the Centre de Recerca Matemàtica (CRM) from March 13 to March 17, 2017. The notes consist of three series of lectures. The first one was given by Dana Williams (Dartmouth College), and served as an introduction to crossed products of C*-algebras and the study of their structure. The second series of lectures was delivered by Aidan Sims (Wollongong), who gave an overview of the theory of topological groupoids (as a model for groups and group actions) and groupoid C*-algebras, with particular emphasis on the case of étale groupoids. Finally, the last series was delivered by Gábor Szabó (Copenhagen), and consisted of an introduction to Rokhlin type properties (mostly centered around the work of Hirshberg, Winter and Zacharias) with hints to the more advanced theory related to groupoids.

Author : Robert Alicki,Institute of Theoretical Physics and Astrophysics Robert Alicki,M. Fannes
Publisher : Oxford University Press on Demand
Page : 278 pages
File Size : 50,8 Mb
Release : 2001
Category : Mathematics
ISBN : 0198504004

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Quantum Dynamical Systems by Robert Alicki,Institute of Theoretical Physics and Astrophysics Robert Alicki,M. Fannes Pdf

The present book provides a unified and general framework for studying quantum and classical dynamical systems, both finite and infinite, conservative and dissipative. Special attention is paid to the use of statistical and geometrical techniques, such as multitime correlation functions,quantum dynamical entropy, and non-commutative Lyapunov exponents, for systems with a complex evolution. The material is presented in a concise but self-contained and mathematically friendly way. The main ideas are introduced and illustrated by numerous examples which are directly connected to therelevant physics. Suggestions for further reading are included at the end of each chapter. The book addresses graduate students both in physics and mathematics with interests in mathematical aspects of quantum physics and applications of ergodic theory, operator algebras and statistics to physics,but without any prior knowledge of these subjects.

Author : V.I. Arnol'd
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 41,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781475720631

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Mathematical Methods of Classical Mechanics by V.I. Arnol'd Pdf

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Author : W. Thirring
Publisher : Unknown
Page : 128 pages
File Size : 55,5 Mb
Release : 1992-01-01
Category : Electronic
ISBN : 3540536124

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A Course in Mathematical Physics I by W. Thirring Pdf

Author : Gerald Teschl
Publisher : American Mathematical Society
Page : 370 pages
File Size : 53,9 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9781470476410

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Ordinary Differential Equations and Dynamical Systems by Gerald Teschl Pdf

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

Author : W. Thirring
Publisher : Unknown
Page : 128 pages
File Size : 54,9 Mb
Release : 1978
Category : Electronic
ISBN : OCLC:929210110

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A Course in Mathematical Physics by W. Thirring Pdf

Author : A.K. Prykarpatsky,Igorʹ Vladimirovich Mikiti︠u︡k
Publisher : Springer
Page : 566 pages
File Size : 45,6 Mb
Release : 1998-06-30
Category : Mathematics
ISBN : UOM:39015050785701

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by A.K. Prykarpatsky,Igorʹ Vladimirovich Mikiti︠u︡k Pdf

Noting that their research is not yet completed, Prykarpatsky (mathematics, U. of Mining and Metallurgy, Cracow, Poland and mechanics and mathematics, NAS, Lviv, Ukraine) and Mykytiuk (mechanics and mathematics, NAS and Lviv Polytechnic State U., Ukraine) describe some of the ideas of Lie algebra that underlie many of the comprehensive integrability theories of nonlinear dynamical systems on manifolds. For each case they analyze, they separate the basic algebraic essence responsible for the complete integrability and explore how it is also in some sense characteristic for all of them. They cover systems with homogeneous configuration spaces, geometric quantization, structures on manifolds, algebraic methods of quantum statistical mechanics and their applications, and algebraic and differential geometric aspects related to infinite-dimensional functional manifolds. They have not indexed their work.