On chain recurrence classes of endomorphisms of ℙ^{𝕜}

Taflin, Johan

doi:10.1090/proc/15947

On chain recurrence classes of endomorphisms of $\mathbb {P}^k$
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Proc. Amer. Math. Soc. 150 (2022), 3941-3951 Request permission

Abstract:

We prove that the minimal chain recurrence classes of a holomorphic endomorphism of $\mathbb {P}^k$ have finitely many connected components. We also obtain results on arbitrary classes. These strong constraints on the topological dynamics in the phase space are all deduced from the associated action on a space of currents.

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