MPEJ Volume 2, No.4, 33pp
Received: June 19, 1996, Accepted: June 21, 1996
L. H. Eliasson
Absolutely Convergent Series Expansions for Quasi Periodic Motions
ABSTRACT:
CONTENTS.
I. INTRODUCTION.
* The Hamiltonian problem
II. THE CLASSICAL APPROACH TO THE HAMILTONIAN PROBLEM -
ABSOLUTELY DIVERGENT SERIES.
* The formal solution and its series expansion
* "Killing the constants" and the Lindstedt series
* Index sets
* Description of the coefficients
* Convergence and divergence of the formal solution
III. SIEGEL'S METHOD.
* Siegel's first lemma
* Siegel's second lemma
* Siegel's third lemma
IV. GENERALIZATION OF SIEGEL'S FIRST LEMMA.
* Resonances on linear index sets
* An equivalence relation on $ad(\gamma)$
* Generalization of Siegel's first lemma - proposition 4
* The basic compensations
* Proof of proposition 4
V. GENERALIZATION OF SIEGEL'S THIRD LEMMA.
* Resonances on index sets
* Generalization of Siegel's third lemma - proposition 5
VI. ABSOLUTELY CONVERGENT SERIES.
* Interpretation of the series
* "Killing the constants"
* Theorem
* Other examples