5 papers · 1 filter
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…
Archimedean toroidal maps and their minimal almost regular covers
Kostiantyn Drach, Yurii Haidamaka, Mark Mixer +1
The automorphism group of a map acts naturally on its flags (triples of incident vertices, edges, and faces). An Archimedean map on the torus is called almost regular if it has as…
A sausage body is a unique solution for a reverse isoperimetric problem
Roman Chernov, Kostiantyn Drach, Kateryna Tatarko
We consider the class of -concave bodies in ; that is, convex bodies with the property that each of their boundary points supports a tangent ball of radius $1/λ…
Inradius estimates for convex domains in 2-dimensional Alexandrov spaces
Kostiantyn Drach
We obtain sharp lower bounds on the radii of inscribed balls for strictly convex isoperimetric domains lying in a 2-dimensional Alexandrov metric space of curvature bounded below.…
Puzzles and the Fatou-Shishikura injection for rational Newton maps
Kostiantyn Drach, Russell Lodge, Dierk Schleicher +1
We establish a principle that we call the Fatou-Shishikura injection for Newton maps of polynomials: there is a dynamically natural injection from the set of non-repelling periodic…