InhaltsangabeBasic 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.

Basic Material and Asymptotics.- Averaging: the Periodic Case.- Methodology of Averaging.- Averaging: 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.-A. The The History of the Theory of Averaging.- B. A 4-dimensional Example of Hopf Bifurcation.- C. Invariant Manifolds by Averaging.- D. Celestial Mechanics.- E. On Averaging Methods for Partial Differential Equations.- References.- Index of Definitions & Descriptions.