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arXiv · 0809.2116

Remarks on Automorphisms of $\mathbb{C}^* \times \mathbb{C}^*$ and their basins

Liz Raquel Vivas
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Abstract

We study basins of attraction of automorphisms of $\CC^2$ tangent to the identity that fix both axes. Our main result is that, if a well known conjecture about automorphisms of $\CC^*\times\CC^*$ holds, then there are no basins of attraction associated to the non-degenerate characteristic directions (in the sense of Hakim), and therefore we cannot find a Fatou-Bieberbach domain that does not intersect both axis with this method.

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Liz Raquel Vivas. 2008-09-12. Remarks on Automorphisms of $\mathbb{C}^* \times \mathbb{C}^*$ and their basins. https://arxiv.org/abs/0809.2116

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