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Averaging Methods in Nonlinear Dynamical Systems

Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, correctio...

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Main Authors: Sanders, Jan A. (Author, http://id.loc.gov/vocabulary/relators/aut), Verhulst, Ferdinand. (http://id.loc.gov/vocabulary/relators/aut), Murdock, James. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2007.
Edition:2nd ed. 2007.
Series:Applied Mathematical Sciences, 59
Subjects:
Dynamics.
Ergodic theory.
Partial differential equations.
Mathematical physics.
Mathematical analysis.
Analysis (Mathematics).
Dynamical Systems and Ergodic Theory.
Partial Differential Equations.
Theoretical, Mathematical and Computational Physics.
Analysis.
Online Access:https://doi.org/10.1007/978-0-387-48918-6
Table of Contents:
  • Basic Material and Asymptotics
  • Averaging: the Periodic Case
  • Methodology of Averaging
  • Averaging: the General Case
  • Attraction
  • Periodic Averaging and Hyperbolicity
  • Averaging over Angles
  • Passage Through Resonance
  • From Averaging to Normal Forms
  • Hamiltonian Normal Form Theory
  • Classical (First-Level) Normal Form Theory
  • Nilpotent (Classical) Normal Form
  • Higher-Level Normal Form Theory
  • The History of the Theory of Averaging
  • A 4-Dimensional Example of Hopf Bifurcation
  • Invariant Manifolds by Averaging
  • Some Elementary Exercises in Celestial Mechanics
  • On Averaging Methods for Partial Differential Equations.

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