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Abundance of escaping orbitsin a family of anti-integrable limitsof the standard map

dc.contributor.advisorDolgopyat, Dmitryen_US
dc.contributor.authorDe Simoi, Jacopoen_US
dc.date.accessioned2010-02-19T06:49:32Z
dc.date.available2010-02-19T06:49:32Z
dc.date.issued2009en_US
dc.identifier.urihttp://hdl.handle.net/1903/9899
dc.description.abstractWe give quantitative results about the abundance of escaping orbits in a family of exact twist maps preserving Lebesgue measure on the cylinder <bold>T</bold> × <bold>R</bold>; geometrical features of maps of this family are quite similar to those of the well-known Chirikov-Taylor standard map, and in fact we believe that the techniques presented in this work can be further improved and eventually applied to studying ergodic properties of the standard map itself. We state conditions which assure that escaping orbits exist and form a full Hausdor&#64256; dimension set. Moreover, under stronger conditions we can prove that such orbits are not charged by the invariant measure. We also obtain prove that, generically, the system presents elliptic islands at arbitrarily high values of the action variable and provide estimates for their total measure.en_US
dc.titleAbundance of escaping orbitsin a family of anti-integrable limitsof the standard mapen_US
dc.typeDissertationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentMathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolleddynamical systemsen_US
dc.subject.pquncontrolledFermi accelerationen_US
dc.subject.pquncontrolledhyperbolic dynamicsen_US


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