44 citations · 231 across the 34 of their papers we have counts for
10 papers · 1 filter
An analogue of a theorem of Kurzweil
David Simmons
A theorem of Kurzweil ('55) on inhomogeneous Diophantine approximation states that if is an irrational number, then the following are equivalent: (A) for every decreasing posit…
Geometric Limits of Julia Sets with Parameters on the Circle
Scott R. Kaschner, Reaper Romero, David Simmons
We show that the geometric limit as of the filled Julia sets for the maps does not exist for almost every on the unit…
Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions
Lior Fishman, Bill Mance, David Simmons +1
We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the non-autonomous dynamical system on the interval $[0…
Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind
Lior Fishman, David Simmons, Mariusz Urbański
We consider the relation between geometrically finite groups and their limit sets in infinite-dimensional hyperbolic space. Specifically, we show that a rigidity theorem of Susskin…
Geometry and dynamics in Gromov hyperbolic metric spaces: With an emphasis on non-proper settings
Tushar Das, David Simmons, Mariusz Urbański
Our monograph presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Our work unifies and extends a long list of r…
A Danzer set for Axis Parallel Boxes
David Simmons, Yaar Solomon
We present concrete constructions of discrete sets in () that intersect every aligned box of volume in , and which have optimal growth rate…