85 citations · 95 across the 8 of their papers we have counts for
8 papers
The dynamics of complex box mappings
Trevor Clark, Kostiantyn Drach, Oleg Kozlovski +1
In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the retur…
Asymmetric unimodal maps with non-universal period-doubling scaling laws
Oleg Kozlovski, Sebastian van Strien
We consider a family of strongly-asymmetric unimodal maps of the form where is unimodal, , is o…
On the structure of isentropes of real polynomials
Oleg Kozlovski
In this paper we will modify the Milnor--Thurston map, which maps a one dimensional mapping to a piece-wise linear of the same entropy, and study its properties. This will allow us…
Cyclicity in families of circle maps
O Kozlovski
In this paper we will study families of circle maps of the form and investigate how many periodic trajectories maps from this family can have fo…
Higher order Schwarzian derivatives in interval dynamics
O. Kozlovski, D. Sands
We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps…
Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials
Oleg Kozlovski, Sebastian van Strien
We prove that topologically conjugate non-renormalizable polynomials are quasi-conformally conjugate. From this we derive that each such polynomial can be approximated by a hyperbo…