KAM-tori near an analytic elliptic fixed point View Full Text


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Article Info

DATE

2013-11

AUTHORS

L. Hakan Eliasson, Bassam Fayad, Raphaël Krikorian

ABSTRACT

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector ω0 is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a Rüssmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that ω0 has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least d + 1 passing through 0 that is foliated by complex analytic KAM-tori with frequency ω0. This is an extension of previous results obtained in [1] to the case of an elliptic fixed point. More... »

PAGES

801-831

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s1560354713060154

DOI

http://dx.doi.org/10.1134/s1560354713060154

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1004754839


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