5 papers
Dynamics of simply parabolic inner functions
Oleg Ivrii
We study the dynamics of Polya-Szegö inner functions and discuss some of their basic properties such as equivalent conditions for simple and double parabolicity. We show that a si…
Inner Functions, Composition Operators, Symbolic Dynamics and Thermodynamic Formalism
Oleg Ivrii, Mariusz UrbaÅski
In this paper, we use thermodynamic formalism to study the dynamics of inner functions acting on the unit disk. If the Denjoy-Wolff point of is in the open unit disk, then…
Analytic mappings of the unit disk with bounded compression
Oleg Ivrii, Artur Nicolau
In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give se…
Analytic mappings of the unit disk which almost preserve hyperbolic area
Oleg Ivrii, Artur Nicolau
In this paper, we study analytic self-maps of the unit disk which distort hyperbolic area of large hyperbolic disks by a bounded amount. We give a number of characterizations invol…
Inner Functions and Laminations
Oleg Ivrii, Mariusz UrbaÅski
In this paper, we study orbit counting problems for inner functions using geodesic and horocyclic flows on Riemann surface laminations. For a one component inner function of finite…