44 citations · 231 across the 34 of their papers we have counts for
5 papers · 2 filters
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…
On interpreting Patterson--Sullivan measures of geometrically finite groups as Hausdorff and packing measures
David Simmons
We provide a new proof of a theorem whose proof was sketched by Sullivan ('82), namely that if the Poincaré exponent of a geometrically finite Kleinian group is strictly betwee…