35 citations · 339 across the 46 of their papers we have counts for
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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…
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…
Rigidity of Newton dynamics
Kostiantyn Drach, Dierk Schleicher
We study rigidity of rational maps that come from Newton's root finding method for polynomials of arbitrary degrees. We establish dynamical rigidity of these maps: each point in th…
Homotopy Hubbard Trees for post-singularly finite exponential maps
David Pfrang, Michael Rothgang, Dierk Schleicher
We extend the concept of a Hubbard tree, well established and useful in the theory of polynomial dynamics, to the dynamics of transcendental entire functions. We show that Hubbard…