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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168993We 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.6 pages, comments welcomeComplex VariablesDynamical Systems32H50 (Primary); 32H02 (Secondary)Remarks on Automorphisms of $\mathbb{C}^* \times \mathbb{C}^*$ and their basinstext