Preperiodic dynatomic curves for $z\mapsto z^d+c$

Yan Gao. "Preperiodic dynatomic curves for $z ↦ z^{d} + c$." Fundamenta Mathematicae 233.1 (2016): 37-69. <http://eudml.org/doc/286217>.

@article{YanGao2016,
abstract = {The preperiodic dynatomic curve $_\{n,p\}$ 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 $_\{n,p\}$ has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of $_\{n,p\}$. We also compute the genus of each component and the Galois group of the defining polynomial of $_\{n,p\}$.},
author = {Yan Gao},
journal = {Fundamenta Mathematicae},
keywords = {dynatomic curves; smooth; irreducible; multibrot set; Galois group; complex dynamics},
language = {eng},
number = {1},
pages = {37-69},
title = {Preperiodic dynatomic curves for $z ↦ z^\{d\} + c$},
url = {http://eudml.org/doc/286217},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Yan Gao
TI - Preperiodic dynatomic curves for $z ↦ z^{d} + c$
JO - Fundamenta Mathematicae
PY - 2016
VL - 233
IS - 1
SP - 37
EP - 69
AB - The preperiodic dynatomic curve $_{n,p}$ 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 $_{n,p}$ has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of $_{n,p}$. We also compute the genus of each component and the Galois group of the defining polynomial of $_{n,p}$.
LA - eng
KW - dynatomic curves; smooth; irreducible; multibrot set; Galois group; complex dynamics
UR - http://eudml.org/doc/286217
ER -