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The dynamical Manin–Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of
$(\mathbb{P}^{1})^{n}$
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 7 / July 2018
- Published online by Cambridge University Press:
- 21 May 2018, pp. 1441-1472
- Print publication:
- July 2018
-
- Article
- Export citation
-
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.
