7 citations · 27 across the 12 of their papers we have counts for
16 papers
The horizontal chord set: to CIRM and back
Diana Davis, Serge Troubetzkoy
We study the set of lengths of the horizontal chords of a continuous function. We give a new proof of Hopf's characterization of this set, and show that it implies that no matter w…
Hyperbolic Staircases: Periodic Paths on -gons
Mei Rose Connor, Diana Davis, Paige Helms +4
The study of polygonal billiards, particularly those in the regular pentagon, has been the subject of two recent papers. One of these papers approaches the problem of discovering t…
The Shape of Thurston's Master Teapot
Harrison Bray, Diana Davis, Kathryn Lindsey +1
We establish basic geometric and topological properties of Thurston's Master Teapot and the Thurston set for superattracting unimodal self-maps of intervals. In particular, the Mas…
Periodic paths on the pentagon, double pentagon and golden L
Diana Davis, Samuel Lelièvre
We give a tree structure on the set of all periodic directions on the golden L, which gives an associated tree structure on the set of periodic directions for the pentagon billiard…
Tiling Billards on Triangle Tilings, and Interval Exchange Transformations
Paul Baird-Smith, Diana Davis, Elijah Fromm +1
We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the be…
How to hear the shape of a billiard table
Aaron Calderon, Solly Coles, Diana Davis +2
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods…