#### Vol. 311, No. 2, 2021

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Dynamical height growth: left, right, and total orbits

Vol. 311 (2021), No. 2, 329–367
##### Abstract

Let $S$ be a set of dominant rational self-maps on ${ℙ}^{N}$. 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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##### Keywords
arithmetic dynamics, heights, random iteration
##### Mathematical Subject Classification
Primary: 11G50, 37A50, 37P15
Secondary: 11R32
##### Milestones
Revised: 22 October 2020
Accepted: 14 January 2021
Published: 31 July 2021
##### Authors
 Wade Hindes Texas State University San Marcos, TX United States