Positive measure of KAM tori for finitely differentiable Hamiltonians

Abed Bounemoura

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arXiv · 1812.03067

Positive measure of KAM tori for finitely differentiable Hamiltonians

Abed Bounemoura

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Abstract

Consider an integer $n \geq 2$ and real numbers $\tau>n-1$ and $l>2(\tau+1)$. Using ideas of Moser, Salamon proved that individual Diophantine tori persist for Hamiltonian systems which are of class $C^l$. Under the stronger assumption that the system is a $C^{l+\tau}$ perturbation of an analytic integrable system, P{\"o}schel proved the persistence of a set of positive measure of Diophantine tori. We improve the last result by showing it is sufficient for the perturbation to be of class $C^{l}$ and the integrable part to be of class $C^{l+2}$.

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Abed Bounemoura. 2018-12-07. Positive measure of KAM tori for finitely differentiable Hamiltonians. https://arxiv.org/abs/1812.03067

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