2 papers
math.CV2025
Rational lemniscates and the matching problem
Kirill Lazebnik, Pierre-Olivier Parisé, Malik Younsi
The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the…
math.DS2025
Classification of Principle 3D Slices of Filled-in Julia Sets in Multicomplex Spaces
Quentin Charles, Pierre-Olivier Parisé
A generalization of the filled-in Julia set is presented using the multicomplex numbers and an algorithm is presented to visualize these sets in the tridimensional space. There are…