Self-maps of projective bundles on projective spaces
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.
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