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dc.contributor.authorFéjoz, Jacques
dc.contributor.authorGuardia, Marcel
dc.contributor.authorKaloshin, Vadim
dc.contributor.authorRoldán, Pablo
dc.date.accessioned2018-02-12T14:02:31Z
dc.date.available2018-02-12T14:02:31Z
dc.date.issued2016
dc.identifier.issn1435-9855
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17380
dc.language.isoenen
dc.subjectThree-body problemen
dc.subjectinstabilityen
dc.subjectresonanceen
dc.subjecthyperbolicityen
dc.subjectMather mechanismen
dc.subjectArnol’d diffusionen
dc.subjectSolar Systemen
dc.subjectAsteroid Belten
dc.subjectKirkwood gapen
dc.subject.ddc515en
dc.titleKirkwood gaps and diffusion along mean motion resonances in the restricted planar three-body problemen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the dynamics of the restricted planar three-body problem near mean motion resonances, i.e. a resonance involving the Keplerian periods of the two lighter bodies revolving around the most massive one. This problem is often used to model Sun--Jupiter--asteroid systems. For the primaries (Sun and Jupiter), we pick a realistic mass ratio μ=10−3 and a small eccentricity e0>0. The main result is a construction of a variety of non local diffusing orbits which show a drastic change of the osculating (instant) eccentricity of the asteroid, while the osculating semi major axis is kept almost constant. The proof relies on the careful analysis of the circular problem, which has a hyperbolic structure, but for which diffusion is prevented by KAM tori. We verify certain non-degeneracy conditions numerically. Based on the work of Treschev, it is natural to conjecture that diffusion time for this problem is ∼−ln(μe0)μ3/2e0. We expect our instability mechanism to apply to realistic values of e0 and we give heuristic arguments in its favor. If so, the applicability of Nekhoroshev theory to the three-body problem as well as the long time stability become questionable. It is well known that, in the Asteroid Belt, located between the orbits of Mars and Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly at mean motion resonances of low order. Our mechanism gives a possible explanation of their existence. To relate the existence of Kirkwood gaps with Arnold diffusion, we state a conjecture on its existence for a typical \eps-perturbation of the product of a pendulum and a rotator. Namely, we predict that a positive conditional measure of initial conditions concentrated in the main resonance exhibits Arnold diffusion on time scales −ln\eps\eps2.en
dc.relation.isversionofjnlnameJournal of the European Mathematical Society
dc.relation.isversionofjnlvol18en
dc.relation.isversionofjnlissue10en
dc.relation.isversionofjnldate2016-09
dc.relation.isversionofjnlpages2313-2401en
dc.relation.isversionofdoi10.4171/JEMS/642en
dc.relation.isversionofjnlpublisherEuropean Mathematical Societyen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-02-12T13:50:52Z
hal.person.labIds60$$$153
hal.person.labIds462618
hal.person.labIds54156
hal.person.labIds210115


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