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  • One-Parameter Deformations of the Bowen-Series Map Associated to Cocompact Triangle Groups

    Creator:
    Yiltekin-Karatas, Ayse
    Abstract:
    In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on the unit circle tightly associated with this group. In general, their fundamental domain enjoys what has since been...
    Resource Type:
    Dissertation
    Full Text:
    approved: Thomas A. Schmidt In 1979, for each signature for Fuchsian groups of the first kind, Bowen and

  • Explicit Dynamical Systems on the Sierpiński Curve

    Creator:
    Homsomboon, Worapan
    Resource Type:
    Dissertation
    Full Text:
    : Explicit Dynamical Systems on the Sierpiński Curve Abstract approved: Thomas A. Schmidt The Sierpiński

  • A New Algorithm for Computing the Veech Group of a Translation Surface

    Creator:
    Edwards, Brandon
    Abstract:
    We give a new characterization of elements in the Veech group of a translation surface. This provides a computational test for Veech group membership. We use this computational test in an algorithm that detects when the Veech group is a lattice (has co-finite area), and in this case computes a...
    Resource Type:
    Dissertation
    Full Text:
    Doctor of Philosophy in Mathematics presented on March 17, 2017. Title: A New Algorithm for Computing

  • New Families of pseudo-Anosov Homeomorphisms with Vanishing Sah-Arnoux-Fathi Invariant

    Creator:
    Do, Hieu Trung
    Abstract:
    Translation surfaces can be viewed as polygons with parallel and equal sides identified. An affine homeomorphism φ from a translation surface to itself is called pseudo-Anosov when its derivative is a constant matrix in SL₂(R) whose trace is larger than 2 in absolute value. In this setting, the eigendirections of...
    Resource Type:
    Dissertation
    Full Text:
    Homeomorphisms with Vanishing Sah-Arnoux-Fathi Invariant. Abstract approved: Thomas A. Schmidt Translation

  • Algebraic Pappus Curves

    Creator:
    Hatase, Tatsuhiko
    Abstract:
    We show that Pappus Curves, introduced by R. Schwartz to study his dynamical system in the real projective plane generated by iterated applications of the classical Pappus Theorem, are algebraic exactly in the linear case. Our approach is to use properties of projective curves such as singular points, genus, number...
    Resource Type:
    Dissertation
    Full Text:
    Curves Abstract approved: Thomas A. Schmidt We show that Pappus Curves, introduced by R. Schwartz to

  • Hilbert modular surfaces and uniformizing groups of Klein invariants

    Creator:
    Bell, Andrea Moreira
    Resource Type:
    Dissertation

  • Triangular billiards surfaces and translation covers

    Creator:
    Schmurr, Jason Peter
    Abstract:
    We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers.
    Resource Type:
    Dissertation
    Full Text:
    : Triangular Billiards Surfa es and Translation Covers Abstra t approved: Thomas A. S hmidt We identify all

  • Spectral modular arithmetic

    Creator:
    Saldamli, Gökay
    Abstract:
    In many areas of engineering and applied mathematics, spectral methods provide very powerful tools for solving and analyzing problems. For instance, large to extremely large sizes of numbers can efficiently be multiplied by using discrete Fourier transform and convolution property. Such computations are needed when computing π to millions of...
    Resource Type:
    Dissertation
    Full Text:
    than the optimal asymptotic crossovers of spectral methods. In this dissertation, a new modular