Fixed Points of Expansive Analytic Maps (II)
Final rept. Oct 1990-Jun 1992
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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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.
- Numerical Mathematics