Kolmogorov Theorem Revisited

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor.author	Villanueva Castelltort, Jordi
dc.date	2004
dc.identifier.uri	http://hdl.handle.net/2117/2820
dc.language.iso	eng
dc.rights	Attribution-NonCommercial-NoDerivs 2.5 Generic
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/2.5/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Ergodic theory
dc.subject	Dynamical systems
dc.subject	Kolmogorov Theorem
dc.subject	Sistemes dinàmics diferenciables
dc.subject	Teoria ergòdica
dc.subject	Classificació AMS::37 Dynamical systems and ergodic theory
dc.title	Kolmogorov Theorem Revisited
dc.type	info:eu-repo/semantics/report
dc.description.abstract	Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound turns to be of O(ε1/4), where ε is the size of the perturbation. In this paper, by means of careful (but involved) estimates on Kolmogorov’smethod, we show that this lower bound can be weakened to be of O(ε1/2). This condition coincides with the optimal one of KAM Theorem. Moreover, we also obtain optimal estimates for the distance between the actions of the perturbed and unperturbed tori.