Fatou Bieberbach domains and automorphisms of Ck tangent to the identity
by Vivas, Liz R., Ph.D., UNIVERSITY OF MICHIGAN, 2009, 58 pages; 3382465

Abstract:

We investigate the following question: Is there a biholomorphic map from [special characters omitted] into the set {zw ≠ 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 [special characters omitted] along non-degenerate characteristic directions, for a large class of automorphisms of [special characters omitted] 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 Γ tangent to the other axis to an arbitrarily high degree.

 
AdviserBerit Stensones
SchoolUNIVERSITY OF MICHIGAN
SourceDAI/B 70-10, p. , Dec 2009
Source TypeDissertation
SubjectsMathematics
Publication Number3382465
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