Carsten Lunde Petersen

collaborators

3 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.CV2024

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

Christian Henriksen, Carsten Lunde Petersen, Eva Uhre

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

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

Roots of polynomial sequences in root-sparse regions

Value Distributions of Derivatives of K-regular Polynomial Families

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