Dynamics of transcendental Henon maps. Part II ![[ Back ] [ Back ]](/components/com_simplecalendar/assets/images/back_icon.gif)
- Date:
- 20.09.17
- Times:
- 09:00 to 11:00
- Place:
- IMUB-Universitat de Barcelona
- Speaker:
- Anna Miriam Benini
- University:
- Universitat de Barcelona
Abstract:
In this course we cover the dynamics of transcendental Henon maps. A transcendental Henon map is an automorphisms of $\C^2$ of the form $F(z,w)=(f(z)+aw,z)$ with $f:\C \to \C$ entire transcendental and $a\in\R$.
Classification of recurrent Fatou components. We show that for any invariant recurrent Fatou component $\Omega$ there is a retraction $\rho:\Omega \rightarrow\Sigma\subset \Omega$ where $\Sigma$ is an invariant limit manifold of rank 0, 1 or 2. If $\Sigma $ has rank 0, $\Omega$ is an attracting domain; If $\Sigma$ has rank 2, $\Omega$ is a rotation domain; if $\Sigma$ has rank 1, then it is a rotational surface.