Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system
نویسنده
چکیده
We give a precise statement for KAM theorem in a neighbourhood of an elliptic equilib rium point of a Hamiltonian system If the frequencies of the elliptic point are nonresonant up to a certain order K and a nondegeneracy condition is ful lled we get an estimate for the measure of the complement of the KAM tori in a neighbourhood of given radius Moreover if the frequencies satisfy a Diophantine condition with exponent we show that in a neighbourhood of radius r the measure of the complement is exponentially small in r We also give a related result for quasi Diophantine frequencies which is more useful for practical purposes The results are obtained by putting the system in Birkho normal form up to an appropiate order and the key point relies on giving accurate bounds for its terms
منابع مشابه
Exponentially Small Estimates for Kam Theorem near an Elliptic Equilibrium Point
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