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Filtering by: Contributor advisor sim Schmidt, Thomas A. Remove constraint Contributor advisor sim: Schmidt, Thomas A.

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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
Explicit Dynamical Systems on the Sierpiński Curve

Creator:

Homsomboon, Worapan

Resource Type:

Dissertation
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
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
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
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
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

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Academic Affiliation

Mathematics8
Electrical Engineering and Computer Science1

Advisor

Schmidt, Thomas A.9
Koc, Cetin Kaya1

Commencement Year

Commencement Year range begin – Commencement Year range end

Current results range from 2001 to 2023

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Committee Member

Escher, Christine3
Guo, Ren3
Swisher, Holly3
Flahive, Mary2
Flahive, Mary E.2
more Committee Members »

Creator

Bell, Andrea Moreira1
Do, Hieu Trung1
Edwards, Brandon1
Hatase, Tatsuhiko1
Homsomboon, Worapan1
more Creators »

Date

Date range begin – Date range end

Current results range from 2000 to 2023

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Decade

2020-20292
2010-20193
2000-20094

Degree Field

Mathematics8
Electrical and Computer Engineering1

Degree Level

Doctoral9

Degree Name

Doctor of Philosophy (Ph.D.)9

Language

English [eng]9

License

All rights reserved8

Non-Academic Affiliation

Oregon State University. Graduate School7

Peer Reviewed

No9

Resource Type

Dissertation9

Rights Statement

In Copyright9

Subject

Curves, Algebraic2
Riemann surfaces2
Differentiable dynamical systems1
Galois theory1
Group theory1
more Subjects »

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