New methods for chaotic dynamics / Nikolai Alexandrovich Magnitskii, Sergey Vasilevich Sidorov.

Format:

Book

Author/Creator:

Magnit︠s︡kiĭ, N. A. (Nikolaĭ Aleksandrovich)

Contributor:

Sidorov, Sergey Vasilevich.

Series:

World Scientific series on nonlinear science. Monographs and treatises ; Series A, v. 58.

World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 58

Language:

English

Subjects (All):

Differentiable dynamical systems.

Differential equations.

Dynamics.

Physical Description:

1 online resource (384 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, New Jersey : World Scientific, c2006.

Language Note:

English

Summary:

This book presents a new theory on the transition to dynamical chaos for two-dimensional nonautonomous, and three-dimensional, many-dimensional and infinitely-dimensional autonomous nonlinear dissipative systems of differential equations including nonlinear partial differential equations and differential equations with delay arguments. The transition is described from the Feigenbaum cascade of period doubling bifurcations of the original singular cycle to the complete or incomplete Sharkovskii subharmonic cascade of bifurcations of stable limit cycles with arbitrary period and finally to the

Contents:

Contents ; Preface ; 1. Systems of Ordinary Differential Equations ; 1.1 Basic Definitions and Theorems ; 1.1.1 Fields of directions and their integral curves ; 1.1.2 Vector fields, differential equations, integral and phase curves; 1.1.3 Theorems of existence and uniqueness of solutions

1.1.4 Differentiable dependence of solutions from initial conditions and parameters, the equations in variations1.1.5 Dissipative and conservative systems of differential equations ; 1.1.6 Numerical methods for solution of systems of ordinary differential equations

1.1.7 Ill-posedness of numerical methods in solution of systems of ordinary differential equations 1.2 Singular Points and Their Invariant Manifolds ; 1.2.1 Singular points of systems of ordinary differential equations ; 1.2.2 Stability of singular points and stationary solutions

1.2.3 Invariant manifolds 1.2.4 Singular points of linear vector fields ; 1.2.5 Separatrices of singular points, homoclinic and heteroclinic trajectories, separatrix contours; 1.3 Periodic and Nonperiodic Solutions, Limit Cycles and Invariant Tori; 1.3.1 Periodic solutions ; 1.3.2 Limit cycles ; 1.3.3 Poincare map ; 1.3.4 Invariant tori

1.4 Attractors of Dissipative Systems of Ordinary Differential Equations 1.4.1 Basic definitions ; 1.4.2 Classical regular attractors of dissipative systems of ordinary differential equations ; 1.4.3 Classical irregular attractors of dissipative dynamical systems ; 1.4.4 Dimension of attractors, fractals

2. Bifurcations in Nonlinear Systems of Ordinary Differential Equations

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611924812

9781281924810

1281924814

9789812773517

9812773517

OCLC:

879023948