Integrability and nonintegrability of dynamical systems

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:
Differentiable dynamical systems.
Differential equations, Nonlinear.
SCIENCE > Physics > Mathematical & Computational.
Differentiable dynamical systems
Differential equations, Nonlinear
Online Access:Click for online access
Table of Contents:
  • 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
  • 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
  • 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
  • 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
  • 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

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