On chain recurrence classes of endomorphisms of \mathbb P^k

2021/05/12 by Johan Taflin, Taflin, Johan
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2105.05524

openalex publication_date 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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