Non-degeneracy conditions in KAM theory

H. Hanßmann

doi:10.1016/j.indag.2011.09.005

Non-degeneracy conditions in KAM theory

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Abstract

Persistence of invariant tori in a perturbed dynamical system requires two kinds of conditions to be met. A strong non-resonance condition ensures a dense quasi-periodic orbit on both the unperturbed and the perturbed torus. A non-degeneracy condition enforces a sufficiently large subset of the unperturbed tori to be non-resonant and thus yields persistence. In the past 60 years various such conditions have been formulated and a number of them are reviewed here.

Original language	English
Pages (from-to)	241-256
Number of pages	16
Journal	Indagationes Mathematicae
Volume	22
Issue number	3-4
DOIs	https://doi.org/10.1016/j.indag.2011.09.005
Publication status	Published - 2011

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abstract = "Persistence of invariant tori in a perturbed dynamical system requires two kinds of conditions to be met. A strong non-resonance condition ensures a dense quasi-periodic orbit on both the unperturbed and the perturbed torus. A non-degeneracy condition enforces a sufficiently large subset of the unperturbed tori to be non-resonant and thus yields persistence. In the past 60 years various such conditions have been formulated and a number of them are reviewed here.",

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AB - Persistence of invariant tori in a perturbed dynamical system requires two kinds of conditions to be met. A strong non-resonance condition ensures a dense quasi-periodic orbit on both the unperturbed and the perturbed torus. A non-degeneracy condition enforces a sufficiently large subset of the unperturbed tori to be non-resonant and thus yields persistence. In the past 60 years various such conditions have been formulated and a number of them are reviewed here.

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DO - 10.1016/j.indag.2011.09.005

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JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 3-4

ER -

Non-degeneracy conditions in KAM theory

Abstract

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