Eigenvalues of the Thurston operator

2017/07/06 by Buff, Xavier, Epstein, Adam L., Koch, Sarah · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.01990

Abstract

Let f:\mathbb C→ \mathbb C be a postcritically finite rational map. Let \mathcal Q(\mathbb C) be the space of meromorphic quadratic differentials on \mathbb C with simple poles. We study the set of eigenvalues of the pushforward operator f_*:\mathcal Q(\mathbb C)→ \mathcal Q(\mathbb C). In particular, we show that when f:\mathbb C → \mathbb C is a unicritical polynomial of degree D with periodic critical point, the eigenvalues of f_*:\mathcal Q(\mathbb C)→ \mathcal Q(\mathbb C) are contained in the annulus \(1)/(4D)

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• Rational maps with constant Thurston pullback mapping

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