Athreya, Jayadev SArtiles Calix, Albert Alejandro2024-10-162024-10-162024-10-162024ArtilesCalix_washington_0250E_27281.pdfhttps://hdl.handle.net/1773/52565Thesis (Ph.D.)--University of Washington, 2024The main results of this dissertation are the computation of the limiting distribution of the minimal denominator function, the computation of Chen-Haynes distributions for a broad class of equivariant processes, and the computation of the probability density distribution of short holonomy vectors of Veech surfaces.application/pdfen-USCC BYDiophantine ApproximationErgodic TheoryFlowsHomogeneous DynamicsMinimal Denominator FunctionTranslation SurfaceMathematicsMathematicsThesis