Accession Number:

ADA254737

Title:

Fixed Points of Expansive Analytic Maps (II)

Descriptive Note:

Final rept. Oct 1990-Jun 1992

Corporate Author:

ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

Report Date:

1992-09-01

Pagination or Media Count:

26.0

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.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE