Carsten Lunde Petersen

collaborators

5 papers

math.DS2025

On qc compatibility of satellite copies of the Mandelbrot set: II

Luna Lomonaco, Carsten Lunde Petersen

The Mandelbrot set is a fractal which classifies the behaviour of complex quadratic polynomials. Although its remarkably simple definition: $\mathcal{M}:=\{c \in \mathbb{C}\,|\,Q_c…

math.CV2025

Roots of polynomial sequences in root-sparse regions

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Given a family $(q_{k})_{k}$ of polynomials, we call an open set $U$ root-sparse if the number of zeros of $q_{k}$ is locally uniformly bounded on $U$ . We study the interplay between the…

math.DS2023

Convergence of Equilibrium Measures under $K$ -regular Polynomial Sequences and their Derivatives

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Let $K \subset C$ be non-polar, compact and polynomially convex. We study the limits of equilibrium measures on preimages of compact sets, under $K$ -regular sequences of pol…

math.CV2023

Value Distributions of Derivatives of $K$ -regular Polynomial Families

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Let $Ω \in C$ be a domain such that $K := C ∖ Ω$ is compact and non-polar. Let $g_{Ω}$ be the Green's function with a logarithmic pole at infinity, and let $ω…

math.CV2023

Zero distributions of derivatives of polynomial families centering on a set

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

Suppose $C \subset C$ is compact. Let $q_{k}$ be a sequence of polynomials of degree $n_{k} \to \infty$ , such that the locus of roots of all the polynomials is bounded, and th…

On qc compatibility of satellite copies of the Mandelbrot set: II

Roots of polynomial sequences in root-sparse regions

Convergence of Equilibrium Measures under K-regular Polynomial Sequences and their Derivatives

Value Distributions of Derivatives of K-regular Polynomial Families

Zero distributions of derivatives of polynomial families centering on a set

Convergence of Equilibrium Measures under $K$ -regular Polynomial Sequences and their Derivatives

Value Distributions of Derivatives of $K$ -regular Polynomial Families