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Nonlinear Dynamics
Exploration Through Normal Forms
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This text concentrates on constructing an exposition of the method of normal forms, a mathematical tool which allows one to simplify as much as possible a complex dynamic system and then study the system and its application to ordinary differential equations through perturbation analysis. Many examples are provided as is an introduction to symbolic computing.The Text: Its Scope, Style, and Content.Basic Concepts.Naive Perturbation Theory (NPT).Formalism of Perturbation Expansion.Problems with Eigenvalues That Have Negative Real Part.Normal Form Expansion for Conservative Planar Systems.Dissipa...
This text concentrates on constructing an exposition of the method of normal forms, a mathematical tool which allows one to simplify as much as possible a complex dynamic system and then study the system and its application to ordinary differential equations through perturbation analysis. Many examples are provided as is an introduction to symbolic computing.
The Text: Its Scope, Style, and Content.
Basic Concepts.
Naive Perturbation Theory (NPT).
Formalism of Perturbation Expansion.
Problems with Eigenvalues That Have Negative Real Part.
Normal Form Expansion for Conservative Planar Systems.
Dissipative Planar Systems.
Nonautonomous Oscillatory Systems.
Problems with a Zero Eigenvalue.
Higher-Dimensional Hamiltonian Systems.
Higher-Dimensional Dissipative Systems.
Appendix.
Index.
The Text: Its Scope, Style, and Content.
Basic Concepts.
Naive Perturbation Theory (NPT).
Formalism of Perturbation Expansion.
Problems with Eigenvalues That Have Negative Real Part.
Normal Form Expansion for Conservative Planar Systems.
Dissipative Planar Systems.
Nonautonomous Oscillatory Systems.
Problems with a Zero Eigenvalue.
Higher-Dimensional Hamiltonian Systems.
Higher-Dimensional Dissipative Systems.
Appendix.
Index.