10 citations · 20 across the 9 of their papers we have counts for
14 papers
Dynamics of Hyperbolic Schwarz Reflections
Kirill Lazebnik
We give a conformal mating description for the class of hyperbolic Schwarz reflections with connected and full filled Julia set; this parallels the recent development in seve…
Blaschke Products Sharing a Welding Homeomorphism
Kirill Lazebnik
Given two Blaschke products , of the same degree, a \emph{welding homeomorphism} of , is a circle homeomorphism satisfying $A\c…
Sharp bounds for the valence of certain logharmonic polynomials
Kirill Lazebnik, Erik Lundberg
Consider a logharmonic polynomial; that is, a product of the form , where , are holomorphic polynomials. Assume is linear and denote by the degr…
Rational lemniscates and the matching problem
Kirill Lazebnik, Pierre-Olivier Parisé, Malik Younsi
The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the…
On the Shapes of Rational Lemniscates
Christopher J. Bishop, Alexandre Eremenko, Kirill Lazebnik
A rational lemniscate is a level set of where is rational. We prove that any planar Euler graph can be approximated, in a s…
Analytic and Topological Nets
Kirill Lazebnik
We characterize which planar graphs arise as the pullback, under a rational map , of an analytic Jordan curve passing through the critical values of . We also prove that such…
A Geometric Approach to Polynomial and Rational Approximation
Christopher J. Bishop, Kirill Lazebnik
We strengthen the classical approximation theorems of Weierstrass, Runge and Mergelyan by showing the polynomial and rational approximants can be taken to have a simple geometric s…
Equilateral Triangulations and The Postcritical Dynamics of Meromorphic Functions
Christopher J. Bishop, Kirill Lazebnik, Mariusz Urbański
We show that any dynamics on any planar set discrete in some domain can be realized by the postcritical dynamics of a function holomorphic in , up to a small perturbatio…
Quadrature Domains and the Real Quadratic Family
Kirill Lazebnik
We study several classes of holomorphic dynamical systems associated with quadrature domains. Our main result is that real-symmetric polynomials in the principal hyperbolic compone…
Bers Slices in Families of Univalent Maps
Kirill Lazebnik, Nikolai G. Makarov, Sabyasachi Mukherjee
We construct embeddings of Bers slices of ideal polygon reflection groups into the classical family of univalent functions . This embedding is such that the conformal mating of…
Univalent Polynomials and Hubbard Trees
Kirill Lazebnik, Nikolai G. Makarov, Sabyasachi Mukherjee
We study rational functions of degree such that is univalent in the exterior unit disc, and the image of the unit circle under has the maximal number of cusps ($d…
Oscillating Wandering Domains for Functions with Escaping Singular Values
Kirill Lazebnik
We construct a transcendental entire such that (1) has bounded singular set, (2) has a wandering domain, and (3) each singular value of…
Prescribing the Postsingular Dynamics of Meromorphic Functions
Christopher J. Bishop, Kirill Lazebnik
We show that any dynamics on any discrete planar sequence can be realized by the postsingular dynamics of some transcendental meromorphic function, provided we allow for small…
Univalent Wandering Domains in the Eremenko-Lyubich Class
Núria Fagella, Xavier Jarque, Kirill Lazebnik
We use the folding theorem of Bishop to construct an entire function in class and a wandering domain of such that restricted to is univalent, for all $…