Hyperbolic Equivariants of Rational Maps
| Autor: | Jacobs, Kenneth |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $K$ denote either $\mathbb{R}$ or $\mathbb{C}$. In this article, we introduce two new equivariants associated to a rational map $f\in K(z)$. These objects naturally live on a real hyperbolic space, and carry information about the action of $f$ on $\mathbb{P}^1(K)$. When $K=\mathbb{C}$ we relate the asymptotic behavior of these equivariants to the conformal barycenter of the measure of maximal entropy. We also give a complete description of these objects for rational maps of degree $d=1$. The constructions in this article are based on work of Rumely in the context of rational maps over non-Archimedean fields; similarities between the two theories are highlighted throughout the article. Comment: 36 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|