Integrability and Nonintegrability of Dynamical Systems

Integrability and Nonintegrability of Dynamical Systems
Author :
Publisher : World Scientific
Total Pages : 438
Release :
ISBN-10 : 981281194X
ISBN-13 : 9789812811943
Rating : 4/5 (4X Downloads)

Book Synopsis Integrability and Nonintegrability of Dynamical Systems by : Alain Goriely

Download or read book Integrability and Nonintegrability of Dynamical Systems written by Alain Goriely and published by World Scientific. This book was released on 2001 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space. Contents: Integrability: An Algebraic Approach; Integrability: An Analytic Approach; Polynomial and Quasi-Polynomial Vector Fields; Nonintegrability; Hamiltonian Systems; Nearly Integrable Dynamical Systems; Open Problems. Readership: Mathematical and theoretical physicists and astronomers and engineers interested in dynamical systems.


Integrability and Nonintegrability of Dynamical Systems Related Books

Integrability and Nonintegrability of Dynamical Systems
Language: en
Pages: 438
Authors: Alain Goriely
Categories: Science
Type: BOOK - Published: 2001 - Publisher: World Scientific

DOWNLOAD EBOOK

This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. S
Differential Galois Theory and Non-Integrability of Hamiltonian Systems
Language: en
Pages: 177
Authors: Juan J. Morales Ruiz
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

DOWNLOAD EBOOK

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and t
Integrability of Dynamical Systems: Algebra and Analysis
Language: en
Pages: 390
Authors: Xiang Zhang
Categories: Mathematics
Type: BOOK - Published: 2017-03-30 - Publisher: Springer

DOWNLOAD EBOOK

This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on t
Spinning Tops
Language: en
Pages: 156
Authors: M. Audin
Categories: Mathematics
Type: BOOK - Published: 1999-11-13 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by cl
Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems
Language: en
Pages: 474
Authors: Antonio Giorgilli
Categories: Science
Type: BOOK - Published: 2022-05-05 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent