On the core entropy of Newton maps

Yan Gao (1)

1 SCU - Sichuan University [Chengdu]

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.

Mots clés: extended Newton graph; critical marking; and phrases: core entropy; polynomial; Newton map AMS(2010) Subject Classification: 37B40; 37F10; 37F20

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Yan Gao. On the core entropy of Newton maps. 2019. ⟨hal-02144546⟩