5 papers
On locally distinguishing SierpiÅski dynamical systems
Sergei Merenkov
We prove that there is no local quasiconformal map between the limit set of a convex-cocompact Kleinian group and the Julia set of a postcritically finite rational map, provided th…
Quasiregular maps of SierpiÅski carpet Julia sets
Sergei Merenkov, Letian Shen
We prove that if and are postcritically finite rational maps whose Julia sets , respectively, are SierpiÅski carpets, and if is a quas…
David extension of circle homeomorphisms, welding, mating, and removability
Mikhail Lyubich, Sergei Merenkov, Sabyasachi Mukherjee +1
We provide a David extension result for circle homeomorphisms conjugating two dynamical systems such that parabolic periodic points go to parabolic periodic points, but hyperbolic…
On a question of Kwakkel and Markovic on existence of wandering domains with bounded geometry
Sergei Merenkov
A question of F. Kwakkel and V. Markovic on existence of C^1-diffeomorphisms of closed surfaces that permute a dense collection of domains with bounded geometry is answered in the…
Carathéodory convergence and the conformal type problem
Alexandre Eremenko, Sergei Merenkov
We study Carathéodory convergence for open, simply connected surfaces spread over the sphere and, in particular, provide examples demonstrating that in the Speiser class the confo…