Nikolai Prochorov

activity

20222026

collaborators

5 papers

math.DS2026

Absence of bounded-orbit wandering domains

Nikolai Prochorov, Lasse Rempe, James Waterman

We prove that transcendental entire functions do not have bounded-orbit wandering domains. This answers a long-standing open question. In fact, we prove a more general theorem, est…

math.DS2024

Finite and infinite degree Thurston maps with extra marked points

Nikolai Prochorov

We investigate the family of marked Thurston maps that are defined everywhere on the topological sphere $S^{2}$ , potentially excluding at most countable closed set of essential singu…

math.DS2024

Finite and infinite degree Thurston maps with a small postsingular set

Nikolai Prochorov

We develop the theory of Thurston maps that are defined everywhere on the topological sphere $S^{2}$ with a possible exception of a single essential singularity. We establish an anal…

math.DS2023

Dynamical approximations of postsingularly finite entire maps

Malavika Mukundan, Nikolai Prochorov, Bernhard Reinke

We prove that every postsingularly finite entire map $g$ can be approximated by a sequence of postcritically finite complex polynomials $(g_{n})$ such that their postsingular dynamic…

math.DS2022

Critically fixed Thurston maps: classification, recognition, and twisting

Mikhail Hlushchanka, Nikolai Prochorov

An orientation-preserving branched covering map $f : S^{2} \to S^{2}$ is called a critically fixed Thurston map if $f$ fixes each of its critical points. It was recently shown that…