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A characterization of postcritically minimal Newton maps of complex exponential functions

Published online by Cambridge University Press:  25 January 2018

KHUDOYOR MAMAYUSUPOV
KHUDOYOR MAMAYUSUPOV*
Affiliation:
Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany email k.mamayusupov@jacobs-university.de National Research University Higher School of Economics, Faculty of Mathematics, Usacheva 6, Moscow, Russia
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Abstract

We obtain a unique, canonical one-to-one correspondence between the space of marked postcritically finite Newton maps of polynomials and the space of postcritically minimal Newton maps of entire maps that take the form $p(z)\exp (q(z))$ for $p(z)$, $q(z)$ polynomials and $\exp (z)$, the complex exponential function. This bijection preserves the dynamics and embedding of Julia sets and is induced by a surgery tool developed by Haïssinsky.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 10 , October 2019 , pp. 2855 - 2880
Copyright
© Cambridge University Press, 2018 

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