44 citations · 171 across the 20 of their papers we have counts for
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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…
The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups
Jason Atnip, Hiroki Sumi, Mariusz Urbański
We study skew-product dynamics for a large class of finitely-generated semi--hyperbolic semigroups of rational maps acting on the Riemann sphere, which generalizes both the theory…
Porosity in conformal dynamical systems
Vasileios Chousionis, Mariusz Urbański
In this paper we study various aspects of porosities for conformal fractals. We first explore porosity in the general context of infinite graph directed Markov systems (GDMS), and…
Long hitting times for expanding systems
Łukasz Pawelec, Mariusz Urbański
We prove a new result in the area of hitting time statistics. Currently, there is a lot of papers showing that the first entry times into cylinders or balls are often faster than t…
Quantization dimension for infinite conformal iterated function systems
Jason Atnip, Mrinal Kanti Roychowdhury, Mariusz Urbański
The quantization dimension function for an -conformal measure generated by an infinite conformal iterated function system satisfying the strong open set condition and by a…
Critically Finite Random Maps of an Interval
Jason Atnip, Mariusz Urbański
We consider random multimodal maps with negative Schwarzian derivative, defined on a finite union of closed intervals in , onto the interval with the base spac…
On the dimension spectrum of infinite subsystems of continued fractions
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if is any arithmetic pro…
Random non-hyperbolic exponential maps
Mariusz Urbański, Anna Zdunik
We consider random iteration of exponential entire functions, i.e. of the form , . Assuming that $…
The dimension spectrum of graph directed Markov systems
Vasileios Chousionis, Dmitriy Leykekhman, Mariusz Urbański
In this paper we study the dimension spectrum of general conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We perform a comprehe…
Thermodynamic formalism and integral means spectrum of asymptotic tracts for transcendental entire functions
Volker Mayer, Mariusz Urbański
We provide the full theory of thermodynamic formalism for a very general collection of entire functions in class . This class overlaps with the collection of all entire…
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…
Conformal graph directed Markov systems on Carnot groups
Vasilis Chousionis, Jeremy T. Tyson, Mariusz Urbański
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, we…
Thin annuli property and exponential distribution of return times for Weakly Markov systems
Łukasz Pawelec, Mariusz Urbański, Anna Zdunik
We deal with the problem of asymptotic distribution of first return times to shrinking balls under iteration generated by a large general class of dynamical systems called weakly M…
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…
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…
Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces
Lior Fishman, David S. Simmons, Mariusz Urbański
In this paper, we provide a complete theory of Diophantine approximation in the limit set of a group acting on a Gromov hyperbolic metric space. This summarizes and completes a lon…
Non-autonomous conformal iterated function systems and Moran-set constructions
Lasse Rempe-Gillen, Mariusz Urbański
We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in…
Distance Expanding Random Mappings, Thermodynamic Formalism, Gibbs Measures, and Fractal Geometry
Volker Mayer, Bartlomiej Skorulski, Mariusz Urbański
In this paper we define distance expanding random dynamical systems. We develop the appropriate thermodynamic formalism of such systems. We obtain in particular the existence and u…
Ergodic properties of sub-hyperbolic functions with polynomial Schwarzian derivative
Volker Mayer, Mariusz Urbański
The ergodic theory and geometry of the Julia set of meromorphic functions on the complex plane with polynomial Schwarzian derivative is investigated under the condition that the fo…