Igors Gorbovickis

activity

20102026

most citedAlgebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable

12 citations · 16 across the 14 of their papers we have counts for

collaborators

20 papers

math.DS2026

Renormalization and rigidity of analytic non-linear interval exchange transformations

Nataliya Goncharuk, Igors Gorbovickis, Michael Yampolsky

We construct hyperbolic renormalization horseshoes for analytic generalized interval exchange transformations (GIETs) of bounded type and with bounded geometry, provided their boun…

math.DS2026

Hyperbolicity of renormalization for maps with multiple breaks

Nataliya Goncharuk, Igors Gorbovickis, Michael Yampolsky

We construct hyperbolic horseshoes for piecewise-analytic homeomorphisms of the circle with {\it multiple} break-type singularities, under the assumptions of bounded type rotation…

math.DS2026

Independence of multipliers via degenerations of rational maps

Igors Gorbovickis

Using degenerations of rational maps and local asymptotics of periodic multipliers, we prove that for every $d \geq 2$ , the multipliers of any $2 d - 2$ distinct periodic orbits of degr…

math.DS2024

Independence of multipliers in several variables complex dynamics

Igors Gorbovickis, Johan Taflin

We establish the independence of multipliers for polynomial endomorphisms of $C^{n}$ and endomorphisms of $P^{n} .$ This allows us to extend results about the bifurcatio…

math.DS2023

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.DS2023

Entire maps with rational preperiodic points and multipliers

Xavier Buff, Igors Gorbovickis, Valentin Huguin

Given a number field $K \subset C$ that is not contained in $R$ , we prove the existence of a dense set of entire maps $f \colon \mathbb{C} \rightarrow \m…

math.DS2022

Lower bounds on the Hausdorff dimension of some Julia sets

Artem Dudko, Igors Gorbovickis, Warwick Tucker

We present an algorithm for a rigorous computation of lower bounds on the Hausdorff dimensions of Julia sets for a wide class of holomorphic maps. We apply this algorithm to obtain…

math.DS2021★ 2 cited

Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers

Igors Gorbovickis, Michael Yampolsky

We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of t…

math.DS2020

Accumulation set of critical points of the multipliers in the quadratic family

Tanya Firsova, Igors Gorbovickis

A parameter $c_{0} \in C$ in the family of quadratic polynomials $f_{c} (z) = z^{2} + c$ is a critical point of a period $n$ multiplier, if the map $f_{c_{0}}$ has a periodic orbit of per…

math.DS2020

Complex a priori bounds for Lorenz maps

Denis Gaidashev, Igors Gorbovickis

We construct complex a-priori bounds for certain infinitely renormalizable Lorenz maps. As a corollary, we show that renormalization is a real-analytic operator on the correspondin…

math.DS2019★ 1 cited

Equidistribution of critical points of the multipliers in the quadratic family

Tanya Firsova, Igors Gorbovickis

A parameter $c_{0} \in C$ in the family of quadratic polynomials $f_{c} (z) = z^{2} + c$ is a critical point of a period $n$ multiplier, if the map $f_{c_{0}}$ has a periodic orbit of per…

math.DS2019

Critical points of the multiplier map for the quadratic family

Anna Belova, Igors Gorbovickis

The multiplier $λ_{n}$ of a periodic orbit of period $n$ can be viewed as a (multiple-valued) algebraic function on the space of all complex quadratic polynomials $p_{c} (z) = z^{2} + c$ . We…

math.DS2017

Renormalization for unimodal maps with non-integer exponents

Igors Gorbovickis, Michael Yampolsky

We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global Hyperbolicity of Renormalization conjecture for unimodal…

math.MG2015

The central set and its application to the Kneser-Poulsen conjecture

Igors Gorbovickis

The Kneser-Poulsen conjecture says that if a finite collection of balls in a Euclidean (spherical or hyperbolic) space is rearranged so that the distance between each pair of cente…

math.DS2015

Rigidity, universality,and hyperbolicity of renormalization for critical circle maps with non-integer exponents

Igors Gorbovickis, Michael Yampolsky

We construct a renormalization operator which acts on analytic circle maps whose critical exponent $α$ is not necessarily an odd integer $2 n + 1$ , $n \in N$ . When $α = 2 n + 1$ , our…

math.DS2014

Algebraic independence of multipliers of periodic orbits in the space of rational maps of the Riemann sphere

Igors Gorbovickis

We consider the space of degree $n \geq 2$ rational maps of the Riemann sphere with $k$ distinct marked periodic orbits of given periods. First, we show that this space is irreducibl…

math.DS2013

Parameterizing degree n polynomials by multipliers of periodic orbits

Igors Gorbovickis

We present the following result: consider the space of complex polynomials of degree n>2 with n-1 distinct marked periodic orbits of given periods. Then this space is irreducible a…

math.DS2013★ 12 cited

Algebraic independence of multipliers of periodic orbits in the space of polynomial maps of one variable

Igors Gorbovickis

We consider a space of complex polynomials of degree $n \geq 3$ with $n - 1$ distinguished periodic orbits. We prove that the multipliers of these periodic orbits considered as algebra…

math.MG2010

Strict Kneser-Poulsen conjecture for large radii

Igors Gorbovickis

In this paper we prove the Kneser-Poulsen conjecture for the case of large radii. Namely, if a finite number of points in Euclidean space $E^{n}$ is rearranged so that the distance b…

math.MG2010★ 1 cited

Kneser-Poulsen conjecture for a small number of intersections

Igors Gorbovickis

The Kneser-Poulsen conjecture says that if a finite collection of balls in a d-dimensional Euclidean space is rearranged so that the distance between each pair of centers does not…