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

Han Peters; Liz Raquel Vivas; Erlend Fornæss Wold

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

Han Peters·Liz Raquel Vivas·Erlend Fornæss Wold

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Abstract

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.

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Han Peters, Liz Raquel Vivas, Erlend Fornæss Wold. 2006-09-29. Attracting basins of volume preserving automorphisms of $\mathbb{C}^k$. https://arxiv.org/abs/math/0610001

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