New Methods for Chaotic Dynamics.

New Methods for Chaotic Dynamics.

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 differe...

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Bibliographic Details
Main Author: Magnitskii, Nikolai Alexandrovich
Other Authors: Sidorov, Sergey Vasilevich
Format: eBook
Language:English
Published: Singapore : World Scientific Publishing Company, 2006.
Series:World Scientific series on nonlinear science. Monographs and treatises.
Subjects:
Differentiable dynamical systems.
Differential equations.
Dynamics.
Differentiable dynamical systems
Differential equations
Dynamics
Online Access:Click for online access
Table of 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.

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