BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alessandra Celletti (University of Rome Tor Vergata\, Italy) DTSTART:20210309T150000Z DTEND:20210309T160000Z DTSTAMP:20260423T024649Z UID:CRM-CAMP/33 DESCRIPTION:Title: KAM (computer-assisted) results in Celestial Mechanics: the dissipative spin-orbit problem\nby Alessandra Celletti (University of Rome Tor Ver gata\, Italy) as part of CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis\n\n\nAbstract\nThe existence of invariant tori throu gh Kolmogorov-Arnold-Moser (KAM) theory has been proven in several models of Celestial Mechanics through dedicated analytical proofs combined with c omputer-assisted techniques. After reviewing some of such results\, obtain ed in conservative frameworks\, we present a recent result on the existenc e of invariant attractors for a dissipative model: the spin-orbit problem with tidal torque. This model belongs to the class of conformally symplect ic systems\, which are characterized by the property that they transform t he symplectic form into a multiple of itself. Finding the solution of such systems requires to add a drift parameter.\n\nWe describe a KAM theorem f or conformally symplectic systems in an a-posteriori format: assuming the existence of an approximate solution\, satisfying the invariance equation up to an error term - small enough with respect to explicit condition numb ers\, - then we can prove the existence of a solution nearby. The theorem\ , which does not assume that the system is close to integrable\, yields an efficient algorithm to construct invariant attractors for the spin-orbit problem and it provides accurate estimates of the breakdown threshold of t he invariant attractor.\n\nThis talk refers to joint works with R. Calleja \, J. Gimeno\, and R. de la Llave.\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/33/ END:VEVENT END:VCALENDAR