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- W4387294042 abstract "The question of the total measure of invariant tori in analytic, nearly--integrable Hamiltonian systems is considered. In 1985, Arnol'd, Kozlov and Neishtadt, in the Encyclopaedia of Mathematical Sciences cite{AKN1}, and in subsequent editions, conjectured that in $n=2$ degrees of freedom the measure of the non torus set of general analytic nearly--integrable systems away from critical points is exponentially small with the size $e$ of the perturbation, and that for $nge 3$ the measure is, in general, of order $e$ (rather than $sqrte$ as predicted by classical KAM Theory). In the case of generic natural Hamiltonian systems, we prove lower bounds on the measure of primary and secondary invariant tori, which are in agreement, up to a logarithmic correction, with the above conjectures. The proof is based on a new {sl singular} KAM theory, particularly designed to study analytic properties in neighborhoods of the secular separatrices generated by the perturbation at simple resonances." @default.
- W4387294042 created "2023-10-03" @default.
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- W4387294042 date "2023-09-29" @default.
- W4387294042 modified "2023-10-04" @default.
- W4387294042 title "Singular KAM Theory" @default.
- W4387294042 doi "https://doi.org/10.48550/arxiv.2309.17041" @default.
- W4387294042 hasPublicationYear "2023" @default.
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