We investigate the existence of whiskered tori in some dissipative systems,
called \sl conformally symplectic \rm systems, having the property that they
transform the symplectic form into a multiple 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].Comment: 15 pages, 1 figur