12 citations · 29 across the 8 of their papers we have counts for
10 papers
Stellar foliation structures on surfaces
W. Patrick Hooper, Ferrán Valdez, Barak Weiss
We introduce the notion of a zebra structure on a surface, which is a more general geometric structure than a translation structure or a dilation structure that still gives a direc…
Platonic solids and high genus covers of lattice surfaces
Jayadev S. Athreya, David Aulicino, W. Patrick Hooper
We study the translation surfaces obtained by considering the unfoldings of the surfaces of Platonic solids. We show that they are all lattice surfaces and we compute the topology…
An infinite surface with the lattice property II: Dynamics of pseudo-Anosovs
W. Patrick Hooper
We study the behavior of hyperbolic affine automorphisms of a translation surface which is infinite in area and genus that is obtained as a limit of surfaces built from regular pol…
Periodicity and ergodicity in the trihexagonal tiling
Diana Davis, W. Patrick Hooper
We consider the dynamics of light rays in the trihexagonal tiling where triangles and hexagons are transparent and have equal but opposite indices of refraction. We find that almos…
Rel leaves of the Arnoux-Yoccoz surfaces
W. Patrick Hooper, Barak Weiss
We analyze the rel leaves of the Arnoux-Yoccoz translation surfaces. We show that for any genus , the leaf is dense in the connected component of the stratum $H(g -1 , g…
The rel leaf and real-rel ray of the Arnoux-Yoccoz surface in genus 3
W. Patrick Hooper, Barak Weiss
We analyze the rel leaf of the Arnoux-Yoccoz translation surface in genus 3. We show that the leaf is dense in the stratum but that the real-rel t…
Immersions and the space of all translation structures
W. Patrick Hooper
A translation structure on a surface is an atlas of charts to the plane so that the transition functions are translations. We allow our surfaces to be non-compact and infinite genu…
Immersions and translation structures I: The space of structures on the pointed disk
W. Patrick Hooper
We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive…
Truchet Tilings and Renormalization
W. Patrick Hooper
The Truchet tiles are a pair of square tiles decorated by arcs. When the tiles are pieced together to form a Truchet tiling, these arcs join to form a family of simple curves in th…
Billiards in Nearly Isosceles Triangles
W. Patrick Hooper, Richard Evan Schwartz
We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier ser…