Index Catalog // ScholarsArchive@OSU

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

Principal subgroups of the nonarithmetic Hecke triangle groups and Galois orbits of algebraic curves

Creator:: Smith, Katherine M.
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

ScholarsArchive@OSU

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

Explicit Dynamical Systems on the Sierpiński Curve

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

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

Algebraic Pappus Curves

Hilbert modular surfaces and uniformizing groups of Klein invariants

Principal subgroups of the nonarithmetic Hecke triangle groups and Galois orbits of algebraic curves

Triangular billiards surfaces and translation covers

Spectral modular arithmetic

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