We present results on the existence of quasi-periodic attractors for conformally symplectic systems in non-perturbative regimes. Conformally symplectic systems are characterized by the property that they transform the symplectic form into a multiple of itself. For such systems, finding the solution requires to add a drift parameter. We provide a very explicit quantitative theorem in an a-posteriori format: assuming the existence of an approximate solution, which satisfies an invariance equation up to an error term which is small enough with respect to explicit condition numbers, then we can state the existence of a solution nearby.
The method can also be used to prove the existence of whiskered tori for conformally symplectic systems and to give a characterization of the analyticity domains of the quasi--periodic attractors in the symplectic limit.
The theorem provides also a very efficient algorithm to generate the solution, which can be implemented successfully in model problems and physically meaningful examples.
The content of this talk refers to works in collaboration with R. Calleja and R. de la Llave.
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