The iteration‐approximation decoupling in the reversible KAM theory

General theorems on the persistence of quasiperiodic motions in reversible flows and diffeomorphisms satisfying very weak nondegeneracy conditions are obtained by a new method. The essence of this method is that the reversible system under consideration is embedded in a multiparameter family of reve...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 1995-09, Vol.5 (3), p.552-565
Main Author: Sevryuk, M. B.
Format: Article
Language:English
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Summary:General theorems on the persistence of quasiperiodic motions in reversible flows and diffeomorphisms satisfying very weak nondegeneracy conditions are obtained by a new method. The essence of this method is that the reversible system under consideration is embedded in a multiparameter family of reversible systems, and standard results on Diophantine approximations of dependent quantities are then applied to Whitney‐smooth Cantor foliations of invariant tori of this family. Invariant tori are constructed for all the permissible values of m, p, q (for vector fields V) or m, p, q, P, Q (for diffeomorphisms A) where m is the torus dimension, (q,p) is the type of the reversing involution G, and (Q,P) is the type of the involution AG. The excitation of elliptic normal modes is also considered.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.166125