 193 Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
 Whiskered KAM tori of conformally symplectic systems
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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 nondegeneracy 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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