On the core entropy of Newton maps

Abstract

In this paper, we define the core entropy for postcritically-finite Newton maps and study its continuity within this family. We show that the entropy function is not continuous in this family, which is different from the polynomial case studied by Thurston, Gao, Dudko-Schleicher, Tiozzo [Th+, GT, DS, Ti2], and describe completely the continuity of the entropy function at generic parameters.

Perturbations of graphs for Newton maps

“…The dynamics of f can be characterized by an invariant graph what is so-called Newton graph. Such graph was first constructed in [4] and then applied to study the dynamics of corresponding maps, see [5,8,9,13,14,26]. In this subsection, we state briefly the construction of Newton graphs and list some properties.…”