Fixed Points of Expansive Analytic Maps (II)
Abstract
The main result of this note, the 'Encircling Theorem,' states conditions that assure that an analytic function is expansive in the closed unit disk D and has a fixed point in D. A corollary describes in detail the case of a conformal sap. From a new covering lemma for polynomials further sufficient conditions are deduced that guarantee that a polynomial of degree n, n - 1,2,... , is expansive and has a fixed point in D. On the other hand, an important example shows that for each n > 3 polynomials of degree n exist that cover D but do not have a fixed point in D. Finally, the distribution of the fixed points of any finite Blaschke - product is established.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1992
- Accession Number
- ADA254737
Entities
People
- Charles E. Hansen
- Walter O. Egerland
Organizations
- Ballistic Research Laboratory