38 citations · 46 across the 7 of their papers we have counts for
7 papers
Linear Flows on Translation Prisms
Jayadev S. Athreya, Nicolas Bédaride, W. Patrick Hooper +1
Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat -manifolds which we call translation prisms. Using ideas of Furstenberg and…
The Necker cube surface
W. Patrick Hooper, Pavel Javornik
We study geodesics on the Necker cube surface, , an infinite periodic Euclidean cone surface that is homeomorphic to the plane and is tiled by squares meeting three or s…
The Extrinsic Primitive Torsion Problem
Khalid Bou-Rabee, W. Patrick Hooper
Let be the subgroup generated by th powers of primitive elements in , the free group of rank . We show that is finite if and only if is , , or…
Indiscriminate covers of infinite translation surfaces are innocent, not devious
W. Patrick Hooper, Rodrigo Treviño
We consider the interaction between passing to finite covers and ergodic properties of the straight-line flow on finite area translation surfaces with infinite topological type. In…
Another Veech Triangle
W. Patrick Hooper
We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics
W. Patrick Hooper
We study the symmetries and geodesics of an infinite translation surface which arises as a limit of translation surfaces built from regular polygons, studied by Veech. We find the…
The Invariant Measures of some Infinite Interval Exchange Maps
W. Patrick Hooper
We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of th…