arXiv Open Access 2011

The Schwarzian derivative and polynomial iteration

Hexi Ye

Lihat Sumber

Abstrak

We consider the Schwarzian derivative $S_f$ of a complex polynomial $f$ and its iterates. We show that the sequence $S_{f^n}/d^{2n}$ converges to $-2(\partial G_f)^2$, for $G_f$ the escape-rate function of $f$. As a quadratic differential, the Schwarzian derivative $S_{f^n}$ determines a conformal metric on the plane. We study the ultralimit of these metric spaces.

Topik & Kata Kunci

math.DS

Penulis (1)

Hexi Ye

Format Sitasi

APA MLA BibTeX

Ye, H. (2011). The Schwarzian derivative and polynomial iteration. https://arxiv.org/abs/1105.5598

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2011
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓