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.

    ARITHMETIC DYNAMICS OF QUADRATIC POLYNOMIALS AND DYNAMICAL UNITS

    Thumbnail
    View/Open
    Panraksa_umd_0117E_12498.pdf (289.3Kb)
    No. of downloads: 987

    Date
    2011
    Author
    Panraksa, Chatchawan
    Advisor
    Washington, Lawrence C.
    Metadata
    Show full item record
    Abstract
    The arithmetic dynamics of rational functions have been studied in many contexts. In this thesis, we concentrate on periodic points. For \phi(x)=x^2+c with c rational, we give a parametrization of all points of order 4 in quadratic fields. For a point of order two and a point of order three for a rational function defined over a number field with good reduction outside a set S, it is known that the bilinear form B([x_1, y_1], [x_2, y_2]) = x_1y_2 - x_2y_1 yields a unit in the ring of S-integers of a number field. We prove that this is essentially the only bilinear form with this property. Finally, we give restrictions on the orders of rational periodic points for rational functions with everywhere good reduction.
    URI
    http://hdl.handle.net/1903/11942
    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