 1216 Renato Calleja, Alessandra Celletti, Rafael de la Llave
 Local behavior near quasiperiodic solutions of conformally symplectic systems
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Feb 6, 12

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Abstract. We study the behavior of conformally symplectic systems near rotational Lagrangian tori. We recall that conformally symplectic systems appear for example in mechanical models including a friction proportional to the velocity.
We show that in a neighborhood of these quasiperiodic solutions (either transitive tori of maximal dimension or periodic solutions), one can always find a smooth symplectic change of variables in which the time evolution becomes just a rotation in some direction and a linear contraction in others. In particular quasiperiodic solutions of contractive (expansive) diffeomorphisms are always local attractors (repellors). We present results when the systems are analytic, $C^r$ or $C^\infty$. We emphasize that the results presented here are nonperturbative and apply to systems that are far from integrable; moreover, we do not require any assumption on the frequency and in particular we do not assume any nonresonance condition.
We also show that the system of coordinates can be computed rather explicitly and we provide iterative algorithms, which allow to generalize the notion of "isochrones". We conclude by showing that the above results apply to quasiperiodic conformally symplectic flows.
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