Zobrazeno 1 - 10
of 3 387
pro vyhledávání: '"Hooper W"'
Autor:
Hooper, W. Patrick, Javornik, Pavel
We study geodesics on the Necker cube surface, $\mathbf N$, an infinite periodic Euclidean cone surface that is homeomorphic to the plane and is tiled by squares meeting three or six to a vertex. We ask: When does a geodesic on the surface close? Whe
Externí odkaz:
http://arxiv.org/abs/2310.03115
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 directional foliation of every slope. We are concerned with the question of
Externí odkaz:
http://arxiv.org/abs/2301.03727
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 of the associated Teichm\"uller curves. Using an algorithm that can be
Externí odkaz:
http://arxiv.org/abs/1811.04131
We study an interval exchange transformation of [0,1] formed by cutting the interval at the points 1/n and reversing the order of the intervals. We find that the transformation is periodic away from a Cantor set of Hausdorff dimension zero. On the Ca
Externí odkaz:
http://arxiv.org/abs/1808.09989
Autor:
Hooper, W. Patrick
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 polygons studied by Veech. We find that hyperbolic affine automorphisms a
Externí odkaz:
http://arxiv.org/abs/1803.01741
Autor:
Bou-Rabee, Khalid, Hooper, W. Patrick
Publikováno v:
Algebr. Geom. Topol. 20 (2020) 3329-3376
Let $P_k$ be the subgroup generated by $k$th powers of primitive elements in $F_r$, the free group of rank $r$. We show that $F_2/P_k$ is finite if and only if $k$ is $1$, $2$, or $3$. We also fully characterize $F_2/P_k$ for $k = 2,3,4$. In particul
Externí odkaz:
http://arxiv.org/abs/1708.02093
Autor:
Schieve, Laura A., Byams, Vanessa R., Dupervil, Brandi, Oakley, Meredith A., Miller, Connie H., Soucie, J. Michael, Abe, Karon, Bean, Christopher J., Hooper, W. Craig
Publikováno v:
Morbidity and Mortality Weekly Report: Surveillance Summaries, 2020 Sep 01. 69(5), 1-18.
Externí odkaz:
https://www.jstor.org/stable/26988946
Autor:
Davis, Diana, Hooper, W. Patrick
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 almost every ray of light is dense in a region of a particular form: the re
Externí odkaz:
http://arxiv.org/abs/1609.00772
Autor:
Parks, Edd Winfield
Publikováno v:
The Georgia Review, 1954 Jul 01. 8(2), 241-242.
Externí odkaz:
https://www.jstor.org/stable/41398036
Autor:
Hooper, W. Patrick, Weiss, Barak
Publikováno v:
Sel. Math. New Ser. 24, 875--934 (2018)
We analyze the rel leaves of the Arnoux-Yoccoz translation surfaces. We show that for any genus $g \geq 3$, the leaf is dense in the connected component of the stratum $H(g -1 , g -1)$ to which it belongs, and the one-sided imaginary-rel trajectory o
Externí odkaz:
http://arxiv.org/abs/1508.05363