19-9 Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
Existence of whiskered KAM tori of conformally symplectic systems (762K, PDF) Jan 23, 19
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Abstract. Many physical problems are described by conformally symplectic systems (i.e., systems whose evolution in time transforms a symplectic form into a multiple of itself). We study the existence of whiskered tori in a family $f_\mu$ of conformally symplectic maps depending on parameters $\mu$ (often called \emph{drifts}). We recall that whiskered tori are tori on which the motion is a rotation, but they have as many expanding/contracting directions as allowed by the preservation of the geometric structure. Our main result is formulated in an \emph{a-posteriori} format. We fix $\omega$ satisfying Diophantine conditions. We assume that we are given 1) a value of the parameter $\mu_0$, 2) an embedding of the torus $K_0$ into the phase space, approximately invariant under $f_{\mu_0}$ in the sense that $f_{\mu_0}

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