Dynamical Systems Seminar

Dynamics of Transcendental Henon maps

by Prof. Anna Miriam Benini (Università di Parma)

Sala Conferenze (Centro Di Ricerca Matematica De Giorgi)

Sala Conferenze

Centro Di Ricerca Matematica De Giorgi


Transcendendental Henon maps are automorphisms of $C^2$ with constant Jacobian, of  the form $F(z,w)=(f(z)+\delta w,z)$, with $f$ entire transcendental and $\delta$ complex number. They are a natural  transcendental analogue of the popular class of polynomial Henon maps. Thanks to their special form, and the advanced knowledge of the dynamics of one dimensional maps,  and despite many open questions, transcendental Henon maps form a class of nonpolynomial automorphisms of C^2 for which it is actually possible to prove general  theorems, yet exhibit a variegated dynamical behaviour with many new features with respect to their polynomial counterpart. We will look at both the stable and the chaotic  dynamics of such maps. This is joint work with Leandro Arosio, John Erik Fornaess and Han Peters.