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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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The location of critical points of finite Blaschke products
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by David A. Singer PDF
Conform. Geom. Dyn. 10 (2006), 117-124 Request permission


A theorem of Bôcher and Grace states that the critical points of a cubic polynomial are the foci of an ellipse tangent to the sides of the triangle joining the zeros. A more general result of Siebert and others states that the critical points of a polynomial of degree $N$ are the algebraic foci of a curve of class $N-1$ which is tangent to the lines joining pairs of zeroes. We prove the analogous results for hyperbolic polynomials, that is, for Blaschke products with $N$ roots in the unit disc.
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Additional Information
  • David A. Singer
  • Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106-7058
  • Email:
  • Received by editor(s): January 16, 2006
  • Published electronically: June 7, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 10 (2006), 117-124
  • MSC (2000): Primary 53A35; Secondary 30D50
  • DOI:
  • MathSciNet review: 2223044