Methods of qualitative theory in nonlinear dynamics. Part II / Leonid P. Shilnikov ... [et al.].

Format:

Book

Contributor:

Shilnikov, L. P.

Series:

World Scientific Series on Nonlinear Science Series A

World scientific series on nonlinear science. Series A, Monographs and treatises ; 5

Language:

English

Subjects (All):

Nonlinear theories.

Nonlinear mechanics.

Physical Description:

1 online resource (591 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, 2001.

Language Note:

English

Summary:

Bifurcation and chaos has dominated research in nonlinear dynamics for over two decades, and numerous introductory and advanced books have been published on this subject. There remains, however, a dire need for a textbook which provides a pedagogically appealing yet rigorous mathematical bridge between these two disparate levels of exposition. This book has been written to serve that unfulfilled need. Following the footsteps of Poincaré, and the renowned Andronov school of nonlinear oscillations, this book focuses on the <i>qualitative</i> study of <i>high-dimensional</i> nonlinear dynamical

Contents:

Contents ; Introduction to Part II ; Chapter 7. STRUCTURALLY STABLE SYSTEMS ; 7.1. Rough systems on a plane. Andronov-Pontryagin theorem ; 7.2. The set of center motions ; 7.3. General classification of center motions ; 7.4. Remarks on roughness of high-order dynamical systems

7.5. Morse-Smale systems 7.6. Some properties of Morse-Smale systems ; Chapter 8. BIFURCATIONS OF DYNAMICAL SYSTEMS ; 8.1. Systems of first degree of non-roughness ; 8.2. Remarks on bifurcations of multi-dimensional systems

8.3. Structurally unstable homoclinic and heteroclinic orbits. Moduli of topological equivalence 8.4. Bifurcations in finite-parameter families of systems. Andronov's setup ; Chapter 9. THE BEHAVIOR OF DYNAMICAL SYSTEMS ON STABILITY BOUNDARIES OF EQUILIBRIUM STATES

9.1. The reduction theorems. The Lyapunov functions 9.2. The first critical case ; 9.3. The second critical case ; Chapter 10. THE BEHAVIOR OF DYNAMICAL SYSTEMS ON STABILITY BOUNDARIES OF PERIODIC TRAJECTORIES ; 10.1. The reduction of the Poincare map. Lyapunov functions

10.2. The first critical case 10.3. The second critical case ; 10.4. The third critical case. Weak resonances ; 10.5. Strong resonances ; 10.6. Passage through strong resonance on stability boundary ; 10.7. Additional remarks on resonances

Chapter 11. LOCAL BIFURCATIONS ON THE ROUTE OVER STABILITY BOUNDARIES

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

ISBN:

9786611948252

9781281948250

128194825X

9789812798558

9812798552

OCLC:

879074291