Unfoldings and Bifurcations of Quasi-Periodic Tori

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Publisher : American Mathematical Soc.
ISBN 13 : 082182483X
Total Pages : 189 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Unfoldings and Bifurcations of Quasi-Periodic Tori by : Hendrik Wolter Broer

Download or read book Unfoldings and Bifurcations of Quasi-Periodic Tori written by Hendrik Wolter Broer and published by American Mathematical Soc.. This book was released on 1990 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I. We consider dynamical systems depending on parameters in various, both conservative and dissipative settings. For such systems integrability is defined as equivariance with respect to an appropriate torus action.

The Symmetry Perspective

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Publisher : Birkhäuser
ISBN 13 : 3034881673
Total Pages : 338 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Symmetry Perspective by : Martin Golubitsky

Download or read book The Symmetry Perspective written by Martin Golubitsky and published by Birkhäuser. This book was released on 2012-12-06 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS

Dynamical Systems and Chaos

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Publisher : Springer Science & Business Media
ISBN 13 : 1441968709
Total Pages : 313 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Dynamical Systems and Chaos by : Henk Broer

Download or read book Dynamical Systems and Chaos written by Henk Broer and published by Springer Science & Business Media. This book was released on 2010-10-20 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.

Mathematical Aspects of Classical and Celestial Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 3540489266
Total Pages : 505 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Mathematical Aspects of Classical and Celestial Mechanics by : Vladimir I. Arnold

Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Global Analysis of Dynamical Systems

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Publisher : CRC Press
ISBN 13 : 9781420034288
Total Pages : 498 pages
Book Rating : 4.0/5 (342 download)

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Book Synopsis Global Analysis of Dynamical Systems by : H.W Broer

Download or read book Global Analysis of Dynamical Systems written by H.W Broer and published by CRC Press. This book was released on 2001-06-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.

Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations

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Publisher : Cambridge University Press
ISBN 13 : 9780521475723
Total Pages : 248 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations by : Jacob Palis Júnior

Download or read book Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations written by Jacob Palis Júnior and published by Cambridge University Press. This book was released on 1995-01-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to the classical theory and its generalizations, aimed at mathematicians and scientists working in dynamical systems.

Handbook of Dynamical Systems

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Publisher : Elsevier
ISBN 13 : 0080932266
Total Pages : 556 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Dynamical Systems by : H. Broer

Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. - Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems - Highlights developments that are the foundation for future research in this field - Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Strange Nonchaotic Attractors: Dynamics Between Order And Chaos In Quasiperiodically Forced Systems

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Publisher : World Scientific
ISBN 13 : 9814478768
Total Pages : 226 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Strange Nonchaotic Attractors: Dynamics Between Order And Chaos In Quasiperiodically Forced Systems by : Arkady S Pikovsky

Download or read book Strange Nonchaotic Attractors: Dynamics Between Order And Chaos In Quasiperiodically Forced Systems written by Arkady S Pikovsky and published by World Scientific. This book was released on 2006-04-26 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph devoted exclusively to strange nonchaotic attractors (SNA), recently discovered objects with a special kind of dynamical behavior between order and chaos in dissipative nonlinear systems under quasiperiodic driving. A historical review of the discovery and study of SNA, mathematical and physically-motivated examples, and a review of known experimental studies of SNA are presented. The main focus is on the theoretical analysis of strange nonchaotic behavior by means of different tools of nonlinear dynamics and statistical physics (bifurcation analysis, Lyapunov exponents, correlations and spectra, renormalization group). The relations of the subject to other fields of physics such as quantum chaos and solid state physics are also discussed.

Normal Forms and Bifurcation of Planar Vector Fields

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Publisher : Cambridge University Press
ISBN 13 : 0521372267
Total Pages : 482 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Normal Forms and Bifurcation of Planar Vector Fields by : Shui-Nee Chow

Download or read book Normal Forms and Bifurcation of Planar Vector Fields written by Shui-Nee Chow and published by Cambridge University Press. This book was released on 1994-07-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary.

Workshop on Dynamical Systems

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Publisher : Longman Scientific and Technical
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Workshop on Dynamical Systems by : E. Shiels

Download or read book Workshop on Dynamical Systems written by E. Shiels and published by Longman Scientific and Technical. This book was released on 1990 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Seminar on Dynamical Systems

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Publisher : Birkhäuser
ISBN 13 : 3034875150
Total Pages : 297 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Seminar on Dynamical Systems by : Lazutkin

Download or read book Seminar on Dynamical Systems written by Lazutkin and published by Birkhäuser. This book was released on 2013-06-29 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The "Dynamical Systems Semester" took place at the Euler International Mathematical Institute in St. Petersburg, Russia, in the autumn of 1991. There were two workshops, October 14-25 and November 18-29, with more than 60 participants giving 70 talks. The titles of all talks are given at the end of this volume. Here we included 22 papers prepared by the authors especially for this volume, while the material of the other talks are published elsewhere. The semester was sponsored by the Soviet Academy of Sciences and UN ESCO. Since the new building of the Euler Institute was not ready at that moment, the sessions were held in the old building of the Steklov Mathemati cal Institute in the very center of St. Petersburg. Members of the staff of the Euler Institute were doing their best to organize properly the normal processing of the conference-not a simple task at that time because of the complications in the political and economical life in Russia just between the coup d'etat in August and the dismantling of the Soviet Union in December. We are thankful to all of them.

Sum of Even Powers of Real Linear Forms

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Publisher : American Mathematical Soc.
ISBN 13 : 0821825232
Total Pages : 169 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Sum of Even Powers of Real Linear Forms by : Bruce Arie Reznick

Download or read book Sum of Even Powers of Real Linear Forms written by Bruce Arie Reznick and published by American Mathematical Soc.. This book was released on 1992 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.

Kernel Functions, Analytic Torsion, and Moduli Spaces

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Publisher : American Mathematical Soc.
ISBN 13 : 082182550X
Total Pages : 137 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Kernel Functions, Analytic Torsion, and Moduli Spaces by : John David Fay

Download or read book Kernel Functions, Analytic Torsion, and Moduli Spaces written by John David Fay and published by American Mathematical Soc.. This book was released on 1992 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and also for the torsion in terms of the Ahlfors-Bers complex structure of the Teichmuller space and Mumford complex structure of the moduli space of stable bundles of degree zero on [italic]C.

Geometric Mechanics and Symmetry

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Publisher : Cambridge University Press
ISBN 13 : 9780521539579
Total Pages : 416 pages
Book Rating : 4.5/5 (395 download)

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Book Synopsis Geometric Mechanics and Symmetry by : James Montaldi

Download or read book Geometric Mechanics and Symmetry written by James Montaldi and published by Cambridge University Press. This book was released on 2005-05-05 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.

Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems

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Publisher : Springer
ISBN 13 : 3540388966
Total Pages : 248 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems by : Heinz Hanßmann

Download or read book Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems written by Heinz Hanßmann and published by Springer. This book was released on 2006-10-18 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.

Perturbation Theory

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Publisher : Springer Nature
ISBN 13 : 1071626213
Total Pages : 601 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Perturbation Theory by : Giuseppe Gaeta

Download or read book Perturbation Theory written by Giuseppe Gaeta and published by Springer Nature. This book was released on 2022-12-16 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

Symmetry and Perturbation Theory

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Author :
Publisher : World Scientific
ISBN 13 : 9812776176
Total Pages : 311 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Symmetry and Perturbation Theory by : Giuseppe Gaeta

Download or read book Symmetry and Perturbation Theory written by Giuseppe Gaeta and published by World Scientific. This book was released on 2008 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is devoted to the interplay of symmetry and perturbation theory, as well as to cognate fields such as integrable systems, normal forms, n-body dynamics and choreographies, geometry and symmetry of differential equations, and finite and infinite dimensional dynamical systems. The papers collected here provide an up-to-date overview of the research in the field, and have many leading scientists in the field among their authors, including: D Alekseevsky, S Benenti, H Broer, A Degasperis, M E Fels, T Gramchev, H Hanssmann, J Krashil''shchik, B Kruglikov, D Krupka, O Krupkova, S Lombardo, P Morando, O Morozov, N N Nekhoroshev, F Oliveri, P J Olver, J A Sanders, M A Teixeira, S Terracini, F Verhulst, P Winternitz, B Zhilinskii. Sample Chapter(s). Foreword (101 KB). Chapter 1: Homogeneous Bi-Lagrangian Manifolds and Invariant Monge-Ampere Equations (415 KB). Contents: On Darboux Integrability (I M Anderson et al.); Computing Curvature without Christoffel Symbols (S Benenti); Natural Variational Principles (D Krupka); Fuzzy Fractional Monodromy (N N Nekhoroshev); Emergence of Slow Manifolds in Nonlinear Wave Equations (F Verhulst); Complete Symmetry Groups and Lie Remarkability (K Andriopoulos); Geodesically Equivalent Flat Bi-Cofactor Systems (K Marciniak); On the Dihedral N-Body Problem (A Portaluri); Towards Global Classifications: A Diophantine Approach (P van der Kamp); and other papers. Readership: Researchers and students (graduate/advanced undergraduates) in mathematics, applied mathematics, physics and nonlinear science.