44 citations · 197 across the 17 of their papers we have counts for
11 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…
On the dimension spectra of infinite iterated function systems
Tushar Das, David Simmons
The dimension spectrum of a conformal iterated function system (CIFS) is the set of all Hausdorff dimensions of its various subsystem limit sets. This brief note provides two const…
Thermodynamic formalism for coarse expanding dynamical systems
Tushar Das, Feliks Przytycki, Giulio Tiozzo +2
We consider a class of dynamical systems, which we call weakly coarse expanding, which is a generalization to the postcritically infinite case of expanding Thurston maps as discuss…
Intersecting limit sets of Kleinian subgroups and Susskind's question
Tushar Das, David Simmons
We construct a non-elementary Fuchsian group that admits two non-elementary subgroups with trivial intersection and whose radial limit sets intersect non-trivially. This negatively…
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…
The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result
Tushar Das, David Simmons
We construct a self-affine sponge in whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hau…
Tukia's isomorphism theorem in CAT(-1) spaces
Tushar Das, David Simmons, Mariusz Urbański
We prove a generalization of Tukia's ('85) isomorphism theorem which states that isomorphisms between geometrically finite groups extend equivariantly to the boundary. Tukia worked…
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…
Dimension rigidity in conformal structures
Tushar Das, David Simmons, Mariusz Urbański
Let be the limit set of a conformal dynamical system, i.e. a Kleinian group acting on either finite- or infinite-dimensional real Hilbert space, a conformal iterated function s…
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…