Fatou Bieberbach Domains and Automorphisms of Ck Tangent to the Identity.

[摘要] We investigate the following question: Is there a biholomorphic map from $CC^2$ into the set ${zw neq 0}$? In order to answer this question we study the construction of Fatou-Bieberbach Domains for maps tangent to the Identity, and we prove that it is not possible to have a Fatou-Bieberbach domain that avoid both axes as the basin of an automorphisms of $CC^2$ along non-degenerate characteristic directions, for a large class of automorphisms of $CC^2$ that fixes both axes. We find new examples of Fatou-Bieberbach domains as basins of attractions of automorphisms tangent to the identity along degenerate characteristic directions. Using a specific map we find a Fatou-Bieberbach domain that avoids one axis and a complex curve $Gamma$ tangent to the other axis to an arbitrarily high degree.

[发布机构] University of Michigan

[效力级别] Automorphisms of C^2 Tangent to the Identity

[关键词] Fatou-Bieberbach Domains;Automorphisms of C^2 Tangent to the Identity;Mathematics;Science;Mathematics