IMAR 75
On the dynamics of polynomial automorphisms of $\mathbb{C}^{2}$
Raluca Tănase
Simion Stoilow Institute of Mathematics of the Romanian Academy
Simion Stoilow Institute of Mathematics of the Romanian Academy
Abstract:
We discuss the dynamics of the complex Hénon map, a prototype of a two-dimensional
dynamical system exhibiting stretching, folding, chaos and various coexisting phenomena,
emphasizing important advances in the field, particularly in the parabolic conservative case.
We discuss the Écalle-Hakim theory for germs tangent to the identity in $\mathbb{C}^{n}$
and its use in the characterization of the Julia set of the Hénon map. Based on joint work
with T. Firsova, R. Radu, J. Raissy, and L. Vivas.