Mean value conjectures for rational maps

DOI10.1080/02781070500293380zbMath1089.30007arXivmath/0411604OpenAlexW2232418255WikidataQ123026205 ScholiaQ123026205MaRDI QIDQ5201533

Edward Crane

Publication date: 19 April 2006

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411604

zbMATH Keywords

distortionrational mapsSmale's mean value conjecture

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10) Real polynomials: analytic properties, etc. (26C05)

Related Items (7)

Almost Newton, sometimes Lattès ⋮ Quadratic and cubic Newton maps of rational functions ⋮ Dynamics and limiting behavior of Julia sets of König's method for multiple roots ⋮ Dynamical aspects of some convex acceleration methods as purely iterative algorithm for Newton's maps ⋮ Convex foliations of degree 5 on the complex projective plane ⋮ On the classification of critically fixed rational maps ⋮ Disconnected Julia set of Halley's method for exponential maps

Cites Work

• Critical points and values of complex polynomials
• Smale's mean value conjecture and the hyperbolic metric
• The fundamental theorem of algebra and complexity theory
• On K nig's root-finding algorithms*

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