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The Cohomological Equation for Horocycle Maps and Quantitative Equidistribution

dc.contributor.advisorForni, Giovannien_US
dc.contributor.authorTanis, James Hollowayen_US
dc.description.abstractThere are infinitely many distributional obstructions to the existence of smooth solutions for the cohomological equation u o φ1 - u = f in each irreducible component of L2(Γ\PSL(2,R)), where φ1 is the time-one map of the horocycle flow. We study the regularity of these obstructions, determine which ones also obstruct the existence of L2 solutions and prove a Sobolev estimate of the solution in terms of f. As an application, we estimate the rate of equidistribution of horocycle maps on compact, finite volume manifolds Γ\PSL(2,R)) using an auxiliary result from Flaminio-Forni (2003) and one from Venkatesh (2010) concerning the horocycle flow and the twisted horocycle flow, respectively.en_US
dc.titleThe Cohomological Equation for Horocycle Maps and Quantitative Equidistributionen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.subject.pquncontrolledDynamical Systemsen_US
dc.subject.pquncontrolledErgodic Theoryen_US
dc.subject.pquncontrolledHarmonic Analysisen_US
dc.subject.pquncontrolledNumber Theoryen_US

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