Iteration at the Boundary of Newton Maps

Abstract

Let $\{N_t\}$ be a holomorphic family of degree $d\ge 3$ Newton maps. By studying the related Berkovich dynamics, we obtain an estimate of the weak limit of the maximal measures of $N_t$. Moreover, we give a complete description of the rescaling limits for $\{N_t\}$.

36 pages, 4 figures

References in corpus (3)

• Rescaling limits of complex rational maps
• Degenerations of Complex Dynamical Systems II: Analytic and Algebraic Stability
• The Geometry of the Minimal Resultant Locus

Cited by in corpus (2)

• Boundedness of Hyperbolic Components of Newton Maps
• Perturbations of graphs for Newton maps