Preperiodic dynatomic curves for $z ↦ z^{d} + c$

• Autorzy: Yan Gao
• Języki publikacji: EN

Abstrakty

EN

The preperiodic dynatomic curve $𝓧_{n,p}$ is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial $z ↦ z^{d} + c$ with preperiod n and period p (n,p ≥ 1). We prove that each $𝓧_{n,p}$ has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of $𝓧_{n,p}$. We also compute the genus of each component and the Galois group of the defining polynomial of $𝓧_{n,p}$.

Kategorie tematyczne

• 37F45: Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
• 37F10: Polynomials; rational maps; entire and meromorphic functions
• 14H50: Plane and space curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 233
• Numer: 1
• Strony: 37-69

Daty

wydano

2016

Twórcy

autor

Yan Gao

• Mathematical School of Sichuan University, ChengDu, 610065, P.R. China

Identyfikatory

DOI

10.4064/fm91-12-2015