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Author: Giampaolo Cicogna
Publisher: Springer Science & Business Media
ISBN: 354048874X
Category : Science
Languages : en
Pages : 218
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Book Description
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: Giampaolo Cicogna
Publisher: Springer Science & Business Media
ISBN: 3540659048
Category : Language Arts & Disciplines
Languages : en
Pages : 218
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Book Description
This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented and a perturbative approach is also used. Attention is given to the problem of convergence of the normalizing transformation in the presence of symmetry, with some other extensions of the theory. The results are discussed for the general case of dynamical systems and also for the specific Hamiltonian setting.
Author: Giuseppe Gaeta
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789812561367
Category : Science
Languages : en
Pages : 332
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Book Description
- In-depth treatment of recent advances in "choreography" solutions to the N-body problem in classical mechanics - Account of recent advances in the geometric theory of separable and superintegrable systems - A geometric approach to symmetry of differential equations.
Author: Antonio Degasperis
Publisher: World Scientific
ISBN: 9814543160
Category :
Languages : en
Pages : 338
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Book Description
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
Publisher: World Scientific
ISBN: 9812776176
Category : Mathematics
Languages : en
Pages : 311
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Book Description
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: Dario Bambusi
Publisher: World Scientific
ISBN: 9814489727
Category : Science
Languages : en
Pages : 260
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Book Description
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: Sebastian Walcher
Publisher: World Scientific
ISBN: 9814486949
Category : Science
Languages : en
Pages : 306
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Book Description
This is the fourth conference on “Supersymmetry and Perturbation Theory” (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc.
Author: Giuseppe Gaeta
Publisher: World Scientific
ISBN: 9814472476
Category : Science
Languages : en
Pages : 311
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Book Description
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.
Author: Dario Bambusi
Publisher: World Scientific
ISBN: 9812794549
Category : Science
Languages : en
Pages : 260
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Book Description
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: World Scientific
ISBN: 9814481114
Category : Science
Languages : en
Pages : 347
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Book Description
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.
Author: Simonetta Abenda
Publisher:
ISBN:
Category : Perturbation (Mathematics)
Languages : en
Pages : 293
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Book Description
