Attracting basins of volume preserving automorphisms of $\mathbb{C}^k$

Peters, Han; Vivas, Liz Raquel; Wold, Erlend Fornæss

Attracting basins of volume preserving automorphisms of $\mathbb{C}^k$

Authors

Peters, Han

Vivas, Liz Raquel

Wold, Erlend Fornæss

Description

We study toplogical properties of attracting sets for automorphisms of $\mathbb{C}^k$. Our main result is that a generic volume preserving automorphism has a hyperbolic fixed point with a dense stable manifold. We prove the same result for volume preserving maps tangent to the identity. On the other hand, we show that an attracting set can only contain a neighborhood of the fixed point if the fixed point is an attracting fixed point. We will see that the latter does not hold in the non-autonomous setting.
11 pages