Raluca Tanase – Hénon maps and discrete groups

Carte non disponible

Date(s) - 18 janvier 2013

Catégories Pas de Catégories

Consider the set $U+$ of points that escape in forward time under the complex Hénon map $H(x,y) = (p(x) – ay, x)$, where $p$ is a quadratic polynomial. This set can be presented as a quotient of $(C-\bar{D}) \times C$ by a discrete group $G$ of automorphisms isomorphic to $Z[1/2]/Z$. We will show how to extend the group action to $S^1 \times C$ in certain cases, in order to represent the boundary $J+$ of $U+$ as a quotient of $S^1 \times C/G$ by an equivalence relation. We will analyze this extension for Hénon maps that are small perturbations of hyperbolic polynomials with connected Julia sets.