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math.DS2018
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…
math.DS2018
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…