  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
$f_\mu$ of conformally symplectic maps which depend on a drift parameter $\mu$.
  We fix a Diophantine frequency of the torus and we assume to have a drift
$\mu_0$ and an embedding of the torus $K_0$, which satisfy approximately the
invariance equation $f_{\mu_0} \circ K_0 - K_0 \circ T_\omega$ (where
$T_\omega$ denotes the shift by $\omega$). We also assume to have a splitting
of the tangent space at the range of $K_0$ into three bundles. We assume that
the bundles are approximately invariant under $D f_{\mu_0}$ and that the
derivative satisfies some "rate conditions".
  Under suitable non-degeneracy conditions, we prove that there exists
$\mu_\infty$, $K_\infty$ and splittings, close to the original ones, invariant
under $f_{\mu_\infty}$. The proof provides an efficient algorithm to construct
whiskered tori. Full details of the statements and proofs are given in
[CCdlL18].
