On the size of attractors in \mathbbCP^k

2013/04/03 by Sandrine Daurat, Daurat, Sandrine
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1304.0991

openalex publication_date 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a holomorphic endomorphism of \mathbbCP^k having an attracting set A. In this paper, we address the question of the "size" of A in a pluripolar sense. We introduce a conceptually simple framework to have non-algebraic attracting sets. We prove that adding a dimensional condition, these sets support a closed positive current with bounded quasi-potential (which answers a question from T.C. Dinh). Therefore, they are not pluripolar. Moreover, the examples are abundant on \mathbbCP^k.

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