Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • Theses and Dissertations from UMD
    • UMD Theses and Dissertations
    • View Item
    •   DRUM
    • Theses and Dissertations from UMD
    • UMD Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    The Cohomological Equation for Horocycle Maps and Quantitative Equidistribution

    Thumbnail
    View/Open
    Tanis_umd_0117E_12314.pdf (419.0Kb)
    No. of downloads: 409

    Date
    2011
    Author
    Tanis, James Holloway
    Advisor
    Forni, Giovanni
    Metadata
    Show full item record
    Abstract
    There 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.
    URI
    http://hdl.handle.net/1903/11794
    Collections
    • Mathematics Theses and Dissertations
    • UMD Theses and Dissertations

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility