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The dynamical Manin–Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of  $(\mathbb{P}^{1})^{n}$

  • Dragos Ghioca (a1), Khoa D. Nguyen (a2) and Hexi Ye (a3)

We prove Zhang’s dynamical Manin–Mumford conjecture and dynamical Bogomolov conjecture for dominant endomorphisms $\unicode[STIX]{x1D6F7}$ of $(\mathbb{P}^{1})^{n}$ . We use the equidistribution theorem for points of small height with respect to an algebraic dynamical system, combined with an analysis of the symmetries of the Julia set for a rational function.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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