Self-maps of projective bundles on projective spaces
type: Item
instance of: scholarly article
title: Self-maps of projective bundles on projective spaces
zbMATH Open document ID: 1099.37035
author: Marius Dabija
published in: Michigan Mathematical Journal
publication date: 2006-05-26T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.mmj/1133894162
review text: The author mainly proves the following theorem: Let \(\mathbb PE\to\mathbb P^n\) be a projective bundle with nonzero discriminant, and let \(f:\mathbb PE\to\mathbb PE\) be a self-map with topological degree at least 2. Then, (1) \(f\) has well-defined algebraic degree; (2) the Fatou components of \(f\) are Stein and Kobayashi hyperbolic; and (3) when \(\text{rank}(E)\geq 3\), the Julia set of \(f\) is connected.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 32H50
Mathematics Subject Classification ID: 37F50
zbMATH DE Number: 5027169
zbMATH Keywords: self-map
zbMATH Keywords: projective bundle
zbMATH Keywords: projective space
MaRDI profile type: Publication
OpenAlex ID: W2006372315
cites work: Sur le problème de Levi dans certains fibres
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cites work: Extending analytic objects
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DOI: 10.1307/MMJ/1133894162
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description: scientific article