Smooth Invariant Manifolds And Normal Forms

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Smooth Invariant Manifolds And Normal Forms

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Author : Alexander Kopanskii
language : en
Publisher: World Scientific
Release Date : 1994-12-22

Smooth Invariant Manifolds And Normal Forms written by Alexander Kopanskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-22 with Science categories.

This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results obtained so far in the investigation of dynamical systems near an arbitrary invariant submanifold is also given.

Normal Forms And Unfoldings For Local Dynamical Systems

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Author : James Murdock
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-10

Normal Forms And Unfoldings For Local Dynamical Systems written by James Murdock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-10 with Mathematics categories.

The subject of local dynamical systems is concerned with the following two questions: 1. Given an n×n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+··· , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.

Poisson Structures And Their Normal Forms

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Author : Jean-Paul Dufour
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17

Poisson Structures And Their Normal Forms written by Jean-Paul Dufour and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-17 with Mathematics categories.

The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

International Conference On Differential Equations Berlin Germany 1 7 August 1999

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Author : Bernold Fiedler
language : en
Publisher: World Scientific
Release Date : 2000

International Conference On Differential Equations Berlin Germany 1 7 August 1999 written by Bernold Fiedler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Differential equations categories.

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences

Symmetry And Perturbation Theory

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Author : Simonetta Abenda
language : en
Publisher: World Scientific
Release Date : 2002

Symmetry And Perturbation Theory written by Simonetta Abenda and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.

Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and Schrodinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDEs (G Cicogna); Bifurcations in Flow-Induced Vibrations (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Y Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); On the Algebro Geometric Solution of a 3x3 Matrix Riemann-Hilbert Problem (v Enolskii & T Grava); Smooth Normalization of a Vector Field Near an Invariant Manifold ((a Kopanskii); Inverse Problems for SL(2) Lattices (V Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative Equilibria for Simple Mechanical Systems (M R Olmos & M E S Dias); A Spectral Sequences Approach to Normal Forms (J Sanders); Rational Parametrization of Strata in Orbit Spaces of Compact Linear Groups (G Sartori & G Valente); Effective Hamiltonians and Perturbation Theory for Quantum Bound States of Nucleur Motion in Molecules (V Tyuterev); Generalized Hasimoto Transformation and Vector Sine-Gordon Equation (J P Wang); and other papers. Readership: Researchers and graduate students in mathematical and theoretical physics, and nonlinears science.

Dynamical Systems I

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Author : S.Kh. Aranson
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-12-18

Dynamical Systems I written by S.Kh. Aranson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-18 with Mathematics categories.

From the reviews: "The reading is very easy and pleasant for the non-mathematician, which is really noteworthy. The two chapters enunciate the basic principles of the field, ... indicate connections with other fields of mathematics and sketch the motivation behind the various concepts which are introduced.... What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. Another point to notice is the existence of an annotated extended bibliography and a very complete index. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool. I thus strongly recommend to buy this very interesting and stimulating book." Journal de Physique

Symmetry And Perturbation Theory Proceedings Of The International Conference On Spt 2002

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Author : Sebastian Walcher
language : en
Publisher: World Scientific
Release Date : 2003-01-14

Symmetry And Perturbation Theory Proceedings Of The International Conference On Spt 2002 written by Sebastian Walcher and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-14 with Science categories.

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.

Equadiff 99 In 2 Volumes Proceedings Of The International Conference On Differential Equations

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Author : Bernold Fiedler
language : en
Publisher: World Scientific
Release Date : 2000-09-05

Equadiff 99 In 2 Volumes Proceedings Of The International Conference On Differential Equations written by Bernold Fiedler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-05 with Mathematics categories.

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences.

Impulsive Differential Equations

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Author : Anatoli? Mikha?lovich Samo?lenko
language : en
Publisher: World Scientific
Release Date : 1995

Impulsive Differential Equations written by Anatoli? Mikha?lovich Samo?lenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

For researchers in nonlinear science, this work includes coverage of linear systems, stability of solutions, periodic and almost periodic impulsive systems, integral sets of impulsive systems, optimal control in impulsive systems, and more.

Analysis Of Complex Nonlinear Mechanical Systems The A Computer Algebra Assisted Approach With Diskette Of Maple Programming

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Author : Martin Lesser
language : en
Publisher: World Scientific Publishing Company
Release Date : 1995-09-20

Analysis Of Complex Nonlinear Mechanical Systems The A Computer Algebra Assisted Approach With Diskette Of Maple Programming written by Martin Lesser and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-20 with Science categories.

The book covers the fundamentals of the mechanics of multibody systems, i.e., systems of interconnected rigid bodies. A geometric view is emphasized in which the techniques and algorithms are motivated by the picture of the rigid body system as a point in the multidimensional space of all possible configurations. The reader is introduced to computer algebra methods in the form of a system, called Sophia, which is implemented in the Maple symbolic manipulation system. The first chapter provides a motivational introduction to the basic principles and an introduction to Maple. Kinematics based on the idea of tangent vectors to the configuration manifold sets the stage for dynamical analysis. The latter ranges from the Lagrange and Gibbs-Appell to Kane's equations. Coverage includes nonholonomic systems and redundant variable methods. The computer algebra methods included enable the treatment of nontrivial mechanical systems and the development of efficient numerical codes for simulation.