14 citations · 38 across the 15 of their papers we have counts for
21 papers
Critical structures of inner functions II
Oleg Ivrii
We study the correspondence proposed in \cite{critical-structures} between inner functions modulo post-compositions with automorphisms of the unit disk and cyclic subspaces of the…
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 sim…
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…
Inner Functions and Laminations
Oleg Ivrii, Mariusz Urbański
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…
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…
Shapes of infinite conformally balanced trees
Oleg Ivrii, Peter Lin, Steffen Rohde +1
Numerical experiments by Werness, Lee and the third author suggested that dessin d'enfants associated to large trivalent trees approximate the developed deltoid introduced by Lee,…
Inner Functions, Composition Operators, Symbolic Dynamics and Thermodynamic Formalism
Oleg Ivrii, Mariusz Urbański
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…
Critical values of inner functions
Oleg Ivrii, Uri Kreitner
Let be the space of inner functions of finite entropy endowed with the topology of stable convergence. We prove that an inner function possesses a r…
Beurling-Carleson sets, inner functions and a semi-linear equation
Oleg Ivrii, Artur Nicolau
Beurling-Carleson sets have appeared in a number of areas of complex analysis such as boundary zero sets of analytic functions, inner functions with derivative in the Nevanlinna cl…
On meromorphic functions whose image has finite spherical area
Oleg Ivrii
In this paper, we study meromorphic functions on a domain whose image has finite spherical area, counted with multiplicity. The paper is composed of two parts…
Critical structures of inner functions
Oleg Ivrii
A celebrated theorem of M. Heins says that up to post-composition with a Möbius transformation, a finite Blaschke product is uniquely determined by its critical points. K. Dyakonov…
Homogenization of random quasiconformal mappings and random Delauney triangulations
Oleg Ivrii, Vladimir Markovic
In this paper, we solve two problems dealing with the homogenization of random media. We show that a random quasiconformal mapping is close to an affine mapping, while a circle pac…
Simultaneous zero-free approximation and universal optimal polynomial approximants
Catherine Bénéteau, Oleg Ivrii, Myrto Manolaki +1
Let be a closed subset of the unit circle of measure zero. Recently, Beise and Müller showed the existence of a function in the Hardy space for which the partial sums of…
Stable convergence of inner functions
Oleg Ivrii
Let be the set of inner functions whose derivative lies in the Nevanlinna class. In this paper, we discuss a natural topology on where if the…
Prescribing inner parts of derivatives of inner functions
Oleg Ivrii
Let be the set of inner functions whose derivatives lie in Nevanlinna class. In this note, we show that the natural map $F \to \text{Inn}(F'): \mathscr J/\text{Aut}(\m…
Sparse Beltrami coefficients, integral means of conformal mappings and the Feynman-Kac formula
Oleg Ivrii
In this note, we give an estimate for the dimension of the image of the unit circle under a quasiconformal mapping whose dilatation has small support. We also prove an analogous es…
Makarov's principle for the Bloch unit ball
Oleg Ivrii, Ilgiz Kayumov
Makarov's principle relates three characteristics of Bloch functions that resemble the variance of a Gaussian: asymptotic variance, the constant in Makarov's law of iterated logari…
On Makarov's principle in conformal mapping
Oleg Ivrii
We examine several characteristics of conformal maps that resemble the variance of a Gaussian: asymptotic variance, the constant in Makarov's law of iterated logarithm and the seco…
Quasicircles of dimension 1+k^2 do not exist
Oleg Ivrii
A well-known theorem of S. Smirnov states that the Hausdorff dimension of a -quasicircle is at most . Here, we show that the precise upper bound $D(k) = 1+Σ^2 k^2 + \math…
The geometry of the Weil-Petersson metric in complex dynamics
Oleg Ivrii
In this work, we study an analogue of the Weil-Petersson metric on the space of Blaschke products of degree 2 proposed by McMullen. Via the Bers embedding, one may view the Weil-Pe…
Asymptotic variance of the Beurling transform
Kari Astala, Oleg Ivrii, Antti Perälä +1
We study the interplay between infinitesimal deformations of conformal mappings, quasiconformal distortion estimates and integral means spectra. By the work of McMullen, the second…