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Quasi-periodicity of motions and complete integrability of Hamiltonian systems

Published online by Cambridge University Press:  01 December 1998

FRANCESCO FASSÒ
FRANCESCO FASSÒ
Affiliation:
Mathematics Department, UCSC, Santa Cruz, CA 95064, USA Permanent address: Università di Padova, Dipartimento di Matematica Pura e Applicata, Via G. Belzoni 7, 35131 Padova, Italy (e-mail: [email protected]).
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Abstract

Consider a Hamiltonian system with $d$ degrees of freedom whose motions are all linear on tori of some fixed dimension $n\led$ is such a system necessarily completely (or else non-commutatively) integrable? We show that the answer is affirmative under quite broad conditions, but not always, and we provide counterexamples

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 6 , December 1998 , pp. 1349 - 1362
Copyright
1998 Cambridge University Press

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