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# Mathematics > Number Theory

# Title: Dynamical height growth: left, right, and total orbits

(Submitted on 23 Feb 2020)

Abstract: Let $S$ be a set of dominant rational self-maps on $\mathbb{P}^N$. We study the arithmetic and dynamical degrees of infinite sequences of $S$ obtained by sequentially composing elements of $S$ on the right and left. We then apply this insight to dynamical Galois theory.

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