A parametrised version of Moser's modifying terms theorem

Florian Wagener

doi:10.3934/dcdss.2010.3.719

Article Contents

2010, Volume 3, Issue 4: 719-768. Doi: 10.3934/dcdss.2010.3.719

This issue Previous Article KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character Next Article

A parametrised version of Moser's modifying terms theorem

Florian Wagener^1,

1.
CeNDEF, Dept. of Quantitative Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam

Received: April 2009

Revised: May 2010

Published online: August 2010

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Abstract

A sharpened version of Moser's 'modifying terms' KAM theorem is derived, and it is shown how this theorem can be used to investigate the persistence of invariant tori in general situations, including those where some of the Floquet exponents of the invariant torus may vanish. The result is 'structural' and can be applied to dissipative, Hamiltonian, and symmetric vector fields; moreover, we give variants of the result for real analytic, Gevrey regular ultradifferentiable and finitely differentiable vector fields. In the first two cases, the conjugacy constructed in the theorem is shown to be Gevrey smooth in the sense of Whitney on the set of parameters that satisfy a "Diophantine'' non-resonance condition.

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Mathematics Subject Classification: Primary: 37C55; Secondary: 37G99.

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