16 citations · 101 across the 29 of their papers we have counts for
32 papers
Geometry of measures in random systems with complete connections
Eugen Mihailescu, Mariusz Urbanski
We study new relations between countable iterated function systems (IFS) with overlaps, Smale endomorphisms and random systems with complete connections. We prove that stationary m…
Ergodic Theory, Geometric Measure Theory, Conformal Measures and the Dynamics of Elliptic Functions
Janina Kotus, Mariusz Urbanski
The ultimate goal of our book is to present a unified approach to the dynamics, ergodic theory, and geometry of elliptic functions from $\C$ to $\oc$. We consider elliptic function…
Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions
Volker Mayer, Mariusz Urbanski
This text provides an overview of the (geometric) thermodynamic formalism for transcendental meromorphic and entire functions with particular emphasis on geometric/fractal aspects…
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…
Smale endomorphisms over graph-directed Markov systems
Eugen Mihailescu, Mariusz Urbanski
We study Smale skew product endomorphisms (introduced in [27]) now over countable graph directed Markov systems, and we prove the exact dimensionality of conditional measures in fi…
Skew product Smale endomorphisms over countable shifts of finite type
Eugen Mihailescu, Mariusz Urbański
We introduce and study skew product Smale endomorphisms over finitely irreducible topological Markov shifts with countable alphabets. We prove that almost all conditional measures…