An analytic counterexample to the KAM theorem

Authors
Bessi, U
Citation
U. Bessi, An analytic counterexample to the KAM theorem, ERGOD TH DY, 20, 2000, pp. 317-333
Citations number
14
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
01433857 → ACNP
Volume
20
Year of publication
2000
Part
2
Pages
317 - 333
Database
ISI
SICI code
0143-3857(200004)20:<317:AACTTK>2.0.ZU;2-2
Abstract
We study the non-existence of KAM tori for quasi-integrable, analytic Lagra ngians. Let L: T-m x R-m --> R, L(Q, (Q)over dot) = 1/2 \((Q)over dot)(2) h(Q) and let <(omega)over bar> is an element of R-m be a frequency exponen tially close to resonances. We find h analytic of norm arbitrarily small su ch that L has no invariant torus of frequency <(omega)over bar> projecting diffeomorphically on T-m.