The Largest Roots of the Mandelbrot Polynomials

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 50)

Abstract

This paper gives some details of the experimental discovery and partial proof of a simple asymptotic development for the largest magnitude roots of the Mandelbrot polynomials defined by p0(z) = 1 and \(p_{n+1}(z) = zp_{n}^{2}(z) + 1\).

Key words

Asymptotic expansion Eigenvalues Mandelbrot polynomials Periodic points Polynomial zeros 

Mathematics Subject Classifications (2010)

Primary 37F10 Secondary 37F45 41A60 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Applied MathematicsThe University of Western OntarioLondonCanada

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