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We study the holomorphic motions of repelling periodic points in stable families of endomorphisms of \(\mathbb {P}^k(\mathbb {C})\) . In particular, we establish an asymptotic naturally-weighted equidistribution of the graphs associated to such periodic points with respect to natural measures in the space of all holomorphic motions of points in the Julia sets.

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Holomorphic Motions of Weighted Periodic Points

  • 会议论文

  • 发表日期：

    2026年

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  • Fabrizio Bianchi,
  • Maxence Brévard

摘要

We study the holomorphic motions of repelling periodic points in stable families of endomorphisms of \(\mathbb {P}^k(\mathbb {C})\) . In particular, we establish an asymptotic naturally-weighted equidistribution of the graphs associated to such periodic points with respect to natural measures in the space of all holomorphic motions of points in the Julia sets.