19-3 Renato C. Calleja, Alessandra Celletti, Rafael de la Llave

Whiskered KAM tori of conformally symplectic systems (577K, PDF) Jan 22, 19

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Abstract. We investigate the existence of whiskered tori in some dissipative systems, called conformally symplectic systems, having the property that they transform the symplectic form into a mul- tiple of itself. We consider a family fμ of conformally symplectic maps which depend on a drift parameter μ. We fix a Diophantine frequency of the torus and we assume to have a drift μ0 and an embedding of the torus K0 , which satisfy approximately the invariance equation fμ0 ◦K0 −K0 ◦Tω (where Tω denotes the shift by ω). We also assume to have a splitting of the tangent space at the range of K0 into three bundles. We assume that the bundles are approximately invariant under Dfμ0 and that the derivative satisfies some rate conditions . Under suitable non-degeneracy conditions, we prove that there exists μ∞ , K∞ and splittings, close to the original ones, invariant under fμ∞ . The proof provides an efficient algorithm to construct whiskered tori. Full details of the statements and proofs are given in [CCdlL18]

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