83 citations · 293 across the 29 of their papers we have counts for
10 papers · 1 filter
Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism
Tushar Das, Lior Fishman, David Simmons +1
We consider small perturbations of a conformal iterated function system (CIFS) produced by either adding or removing some generators with small derivative from the original. We est…
Badly approximable points on self-affine sponges and the lower Assouad dimension
Tushar Das, Lior Fishman, David Simmons +1
We highlight a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of…
Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems
Tushar Das, Lior Fishman, David Simmons +1
We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalize…
Extremality and dynamically defined measures, part I: Diophantine properties of quasi-decaying measures
Tushar Das, Lior Fishman, David Simmons +1
We present a new method of proving the Diophantine extremality of various dynamically defined measures, vastly expanding the class of measures known to be extremal. This generalize…
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…