Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).

# The dynatomic curves for unimodel polynomials are smooth and irreducible

* Corresponding author
Abstract : We prove here the smoothness and the irreducibility of the periodic dynatomic curves $(c,z)\in \C^2$ such that $z$ is $n$-periodic for $z^d+c$, where $d\geq2$. We use the method provided by Xavier Buff and Tan Lei in \cite{BT} where they prove the conclusion for $d=2$. The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials, following Thurston and Epstein, while the proof for irreducibility is a simplified version of Lau-Schleicher's proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.
Keywords :
Document type :
Preprints, Working Papers, ...

Cited literature [11 references]

https://hal.archives-ouvertes.fr/hal-00814484
Contributor : Yan Gao Connect in order to contact the contributor
Submitted on : Wednesday, April 17, 2013 - 11:35:45 AM
Last modification on : Wednesday, October 20, 2021 - 3:18:43 AM
Long-term archiving on: : Monday, April 3, 2017 - 6:29:09 AM

### Files

periodic_curve.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00814484, version 1
• ARXIV : 1304.4751

### Citation

yan Gao, ya Fei Ou. The dynatomic curves for unimodel polynomials are smooth and irreducible. 2012. ⟨hal-00814484⟩

Record views