83 citations · 137 across the 5 of their papers we have counts for
11 papers
Quantitative results using variants of Schmidt's game: Dimension bounds, arithmetic progressions, and more
Ryan Broderick, Lior Fishman, David Simmons
Schmidt's game is generally used to deduce qualitative information about the Hausdorff dimensions of fractal sets and their intersections. However, one can also ask about quantitat…
Attractors of sequences of iterated function systems
Ryan Broderick
If and are iterated function systems, then any infinite word in the symbols and induces a limit set. It is natural to ask whether this Cantor set can also be re…
Decaying and non-decaying badly approximable numbers
Ryan Broderick, Lior Fishman, David Simmons
We call a badly approximable number if, roughly, the Lagrange constants of integer multiples of that number decay as fast as possible. In this terminology, a question of…
Finite orbits in random subshifts of finite type
Ryan Broderick
For each and , we define a random subset of by independently including each element with probability and ex…
Complexity and directional entropy in two dimensions
Ryan Broderick, Van Cyr, Bryna Kra
We study the directional entropy of the dynamical system associated to a configuration in a finite alphabet. We show that under local assumptions on the complexity, either e…
Dimension estimates for sets of uniformly badly approximable systems of linear forms
Ryan Broderick, Dmitry Kleinbock
The set of badly approximable matrices is known to have Hausdorff dimension . Each such matrix comes with its own approximation constant , and one can ask for…