35 citations · 339 across the 46 of their papers we have counts for
52 papers
A canonical decomposition of postcritically finite rational maps and their maximal expanding quotients
Dzmitry Dudko, Mikhail Hlushchanka, Dierk Schleicher
We provide a natural canonical decomposition of postcritically finite rational maps with non-empty Fatou sets based on the topological structure of their Julia sets. The building b…
Mathematical Proof Between Generations
Jonas Bayer, Christoph Benzmüller, Kevin Buzzard +7
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This…
Filament Pairs, Dynamic Partitions, and Spiders for Post-Singularly Finite Entire Functions
David Pfrang, Sören Petrat, Bernhard Reinke +1
Filaments are a natural generalization of the well-known concept of dynamic rays in complex dynamics. In this article we investigate which periodic or preperiodic filaments land to…
Unicritical Laminations
Sourav Bhattacharya, Alexander Blokh, Dierk Schleicher
Thurston introduced \emph{invariant (quadratic) laminations} in his 1984 preprint as a vehicle for understanding the connected Julia sets and the parameter space of quadratic polyn…
The Weierstrass root finder is not generally convergent
Bernhard Reinke, Dierk Schleicher, Michael Stoll
Finding roots of univariate polynomials is one of the fundamental tasks of numerics, and there is still a wide gap between root finders that are well understood in theory and those…
Finding polynomial roots by dynamical systems -- a case study
Sergey Shemyakov, Roman Chernov, Dzmitry Rumiantsau +3
We investigate two well known dynamical systems that are designed to find roots of univariate polynomials by iteration: the methods known by Newton and by Ehrlich-Aberth. Both are…