Symmetry And Perturbation Theory In Nonlinear Dynamics

Author : Giampaolo Cicogna,Guiseppe Gaeta
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 41,7 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540488743

Get Book

Symmetry and Perturbation Theory in Nonlinear Dynamics by Giampaolo Cicogna,Guiseppe Gaeta Pdf

has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to a equations increasingly popular applied of the of the book Olver This by variety problems (following appearance [2621). with is and deals of nature theory deeply geometrical symmetries general (pro vided that described i.e. in this context there is are vector no they by fields), to limit attention to linear reason symmetries. In this look the basic tools of i.e. normal book we at perturbation theory, introduced Poincar6 about and their inter a forms (first by century ago) study action with with no limitation to linear ones. We focus on the most symmetries, basic fixed the and i.e. a setting, systems having point (at origin) perturbative around thus is local.

Author : Antonio Degasperis,Giuseppe Gaeta
Publisher : World Scientific
Page : 338 pages
File Size : 46,6 Mb
Release : 1999-12-30
Category : Electronic
ISBN : 9789814543163

Get Book

Symmetry And Perturbation Theory: Spt 98 by Antonio Degasperis,Giuseppe Gaeta Pdf

The second workshop on “Symmetry and Perturbation Theory” served as a forum for discussing the relations between symmetry and perturbation theory, and this put in contact rather different communities. The extension of the rigorous results of perturbation theory established for ODE's to the case of nonlinear evolution PDE's was also discussed: here a number of results are known, particularly in connection with (perturbation of) integrable systems, but there is no general frame as solidly established as in the finite-dimensional case. In aiming at such an infinite-dimensional extension, for which standard analytical tools essential in the ODE case are not available, it is natural to look primarily at geometrical and topological methods, and first of all at those based on exploiting the symmetry properties of the systems under study (both the unperturbed and the perturbed ones); moreover, symmetry considerations are in several ways basic to our understanding of integrability, i.e. finally of the unperturbed systems on whose understanding the whole of perturbation theory has unavoidably to rely.This volume contains tutorial, regular and contributed papers. The tutorial papers give students and newcomers to the field a rapid introduction to some active themes of research and recent results in symmetry and perturbation theory.

Author : Giuseppe Gaeta,Raffaele Vitolo,Sebastian Walcher
Publisher : World Scientific
Page : 311 pages
File Size : 55,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812776174

Get Book

Symmetry and Perturbation Theory by Giuseppe Gaeta,Raffaele Vitolo,Sebastian Walcher Pdf

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.

Author : Giuseppe Gaeta,Barbara Prinari,Stefan Rauch-Wojciechowski,Susanna Terracini
Publisher : World Scientific
Page : 344 pages
File Size : 52,7 Mb
Release : 2005-01-25
Category : Science
ISBN : 9789814481113

Get Book

Symmetry and Perturbation Theory by Giuseppe Gaeta,Barbara Prinari,Stefan Rauch-Wojciechowski,Susanna Terracini Pdf

This proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability. The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis. The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko. Contents:Parametric Excitation in Nonlinear Dynamics (T Bakri)Similarity Reductions of an Optical Model (M S Bruzón & M L Gandarias)A Regularity Theory for Optimal Partition Problems (M Conti et al.)Periodic Solutions for Zero Mass Nonlinear Wave Equations (G Gentile)Renormalization Group Symmetry and Gas Dynamics (S Murata)Refined Computation of Hypernormal Forms (J Murdock)Regularity of Pseudogroup Orbits (P J Olver & J Pohjanpelto)On Birkhoff Method for Integrable Lagrangian Systems (G Pucacco)and other papers Readership: Researchers and academics. Keywords:Nonlinear Dynamics;Perturbation;Symmetry;Mathematical Physics;Integrable Systems;Dynamical Systems;Geometry;Classical MechanicsKey Features:In-depth treatment of recent advances in “choreography” solutions to the N-body problem in classical mechanicsAccount of recent advances in the geometric theory of separable and superintegrable systemsA geometric approach to symmetry of differential equations

Author : Dario Bambusi,Giuseppe Gaeta,Mariano Cadoni
Publisher : World Scientific
Page : 260 pages
File Size : 55,8 Mb
Release : 2001
Category : Science
ISBN : 9789812794543

Get Book

Theory and Experiment Heading for New Physics by Dario Bambusi,Giuseppe Gaeta,Mariano Cadoni Pdf

The third conference on ?Symmetry and Perturbation Theory? (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field ? more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit.

Author : Giuseppe Gaeta
Publisher : Springer Nature
Page : 601 pages
File Size : 52,7 Mb
Release : 2022-12-16
Category : Science
ISBN : 9781071626214

Get Book

Perturbation Theory by Giuseppe Gaeta Pdf

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.

Author : Dario Bambusi,Mariano Cadoni,Giuseppe Gaeta
Publisher : World Scientific
Page : 260 pages
File Size : 41,5 Mb
Release : 2001-10-19
Category : Science
ISBN : 9789814489720

Get Book

Symmetry And Perturbation Theory (Spt 2001), Proceedings Of The International Conference by Dario Bambusi,Mariano Cadoni,Giuseppe Gaeta Pdf

The third conference on “Symmetry and Perturbation Theory” (SPT2001) was attended by over 50 mathematicians, physicists and chemists. The proceedings present the advancement of research in this field — more precisely, in the different fields at whose crossroads symmetry and perturbation theory sit.

Author : Laura Menini,Antonio Tornambè
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 42,6 Mb
Release : 2011-05-06
Category : Technology & Engineering
ISBN : 9780857296122

Get Book

Symmetries and Semi-invariants in the Analysis of Nonlinear Systems by Laura Menini,Antonio Tornambè Pdf

This book details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the tools for this, such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a different, less complex and more easily comprehensible manner. They are applied to physically motivated systems, to demonstrate how much insight into known properties is gained using these techniques. Various control systems applications of the techniques are characterized including: computation of the flow of nonlinear systems; computation of semi-invariants; computation of Lyapunov functions for stability analysis and observer design.

Author : Antonio Degasperis,Giuseppe Gaeta
Publisher : World Scientific Publishing Company Incorporated
Page : 321 pages
File Size : 51,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9810241666

Get Book

International Workshop on Symmetry and Perturbation Theory (SPT 98) by Antonio Degasperis,Giuseppe Gaeta Pdf

The second workshop on "Symmetry and Perturbation Theory" served as a forum for discussing the relations between symmetry and perturbation theory, and this put in contact rather different communities. The extension of the rigorous results of perturbation theory established for ODE's to the case of nonlinear evolution PDE's was also discussed: here a number of results are known, particularly in connection with (perturbation of) integrable systems, but there is no general frame as solidly established as in the finite-dimensional case. In aiming at such an infinite-dimensional extension, for which standard analytical tools essential in the ODE case are not available, it is natural to look primarily at geometrical and topological methods, and first of all at those based on exploiting the symmetry properties of the systems under study (both the unperturbed and the perturbed ones); moreover, symmetry considerations are in several ways basic to our understanding of integrability, i.e. finally of the unperturbed systems on whose understanding the whole of perturbation theory has unavoidably to rely. This volume contains tutorial, regular and contributed papers. The tutorial papers give students and newcomers to the field a rapid introduction to some active themes of research and recent results in symmetry and perturbation theory.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 45,6 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

Get Book

Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : H.W. Broer,I. Hoveijn,F. Takens,S.A. van Gils
Publisher : Birkhäuser
Page : 464 pages
File Size : 43,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034875189

Get Book

Nonlinear Dynamical Systems and Chaos by H.W. Broer,I. Hoveijn,F. Takens,S.A. van Gils Pdf

Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.

Author : Sandro Wimberger
Publisher : Springer
Page : 206 pages
File Size : 54,5 Mb
Release : 2014-05-13
Category : Science
ISBN : 9783319063430

Get Book

Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : International Workshop on Symmetry and Perturbation Theory,Aantonio Degasperis,Giuseppe Gaeta
Publisher : Unknown
Page : 321 pages
File Size : 51,8 Mb
Release : 1999
Category : Electronic
ISBN : OCLC:247289127

Get Book

International Workshop on Symmetry and Perturbation Theory by International Workshop on Symmetry and Perturbation Theory,Aantonio Degasperis,Giuseppe Gaeta Pdf

Author : Linda Reichl
Publisher : Springer Nature
Page : 555 pages
File Size : 51,7 Mb
Release : 2021-04-12
Category : Science
ISBN : 9783030635343

Get Book

The Transition to Chaos by Linda Reichl Pdf

Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.

Author : Peter B. Kahn,Yair Zarmi
Publisher : Courier Corporation
Page : 416 pages
File Size : 47,8 Mb
Release : 2014-06-10
Category : Science
ISBN : 9780486795027

Get Book

Nonlinear Dynamics by Peter B. Kahn,Yair Zarmi Pdf

Exposition for advanced undergraduates and graduate students covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. Numerous examples of equations encountered in areas of science and engineering. 1998 edition.