3 papers
math.DS2026
Renormalization and scaling of bubbles
Nataliya Goncharuk, Igors Gorbovickis
The paper explores scaling properties of bubbles -- a complex analogue of Arnold tongues, associated to a one-dimensional family of analytic circle diffeomorphisms. Bubbles are smo…
math.DS2025
Entire maps with rational preperiodic points and multipliers
Xavier Buff, Igors Gorbovickis, Valentin Huguin
Given a number field that is not contained in , we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \m…
math.DS2025
Independence of multipliers in several variables complex dynamics
Igors Gorbovickis, Johan Taflin
We establish the independence of multipliers for polynomial endomorphisms of and endomorphisms of This allows us to extend results about the bifurcatio…