Integrability and nonintegrability of dynamical systems / Alain Goriely.

This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, it...

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Bibliographic Details
Main Author: Goriely, Alain
Format: eBook
Language:English
Published: Singapore ; River Edge, NJ : World Scientific, ©2001.
Series:Advanced series in nonlinear dynamics ; v. 19.
Subjects:
Online Access:Click for online access

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245 1 0 |a Integrability and nonintegrability of dynamical systems /  |c Alain Goriely. 
260 |a Singapore ;  |a River Edge, NJ :  |b World Scientific,  |c ©2001. 
300 |a 1 online resource (xviii, 415 pages) :  |b illustrations 
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490 1 |a Advanced series in nonlinear dynamics ;  |v v. 19 
504 |a Includes bibliographical references (pages 385-409) and index. 
588 0 |a Print version record. 
520 |a This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). 
505 0 |a Preface ; Chapter 1 Introduction ; 1.1 A planar system ; 1.1.1 A dynamical system approach ; 1.1.2 An algebraic approach ; 1.1.3 An analytic approach ; 1.1.4 Relevant questions ; 1.2 The Lorenz system ; 1.2.1 A dynamical system approach ; 1.2.2 An algebraic approach 
505 8 |a 1.2.3 An analytic approach 1.2.4 Relevant questions ; 1.3 Exercises ; Chapter 2 Integrability: an algebraic approach ; 2.1 First integrals ; 2.1.1 A canonical example: The rigid body motion ; 2.2 Classes of functions ; 2.2.1 Elementary first integrals ; 2.2.2 Differential fields 
505 8 |a 2.3 Homogeneous vector fields 2.3.1 Scale-invariant systems ; 2.3.2 Homogeneous and weight-homogeneous decompositions ; 2.3.3 Weight-homogeneous decompositions ; 2.4 Building first integrals ; 2.4.1 A simple algorithm for polynomial first integrals ; 2.5 Second integrals 
505 8 |a 2.5.1 Darboux polynomials 2.5.2 Darboux polynomials for planar vector fields ; 2.5.3 The Prelle-Singer Algorithm ; 2.6 Third integrals ; 2.7 Higher integrals ; 2.8 Class-reduction ; 2.9 First integrals for vector fields in R3: the compatibility analysis ; 2.10 Integrability 
505 8 |a 2.10.1 Local integrability 2.10.2 Liouville integrability ; 2.10.3 Algebraic integrability ; 2.11 Jacobi's last multiplier method ; 2.12 Lax pairs ; 2.12.1 General properties ; 2.12.2 Construction of Lax pairs ; 2.12.3 Completion of Lax pairs ; 2.12.4 Recycling integrable systems 
650 0 |a Differentiable dynamical systems. 
650 0 |a Differential equations, Nonlinear. 
650 7 |a SCIENCE  |x Physics  |x Mathematical & Computational.  |2 bisacsh 
650 7 |a Differentiable dynamical systems  |2 fast 
650 7 |a Differential equations, Nonlinear  |2 fast 
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776 0 8 |i Print version:  |a Goriely, Alain.  |t Integrability and nonintegrability of dynamical systems.  |d Singapore ; River Edge, NJ : World Scientific, ©2001  |z 981023533X  |z 9789810235338  |w (OCoLC)41925060 
830 0 |a Advanced series in nonlinear dynamics ;  |v v. 19. 
856 4 0 |u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=1679292  |y Click for online access 
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