3 papers
math.CV2020
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…
math.DS2019
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…
math.CV2018
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…