Dynamical height growth: left, right, and total orbits

Wade Hindes

Vol. 311 (2021), No. 2, 329–367

DOI: 10.2140/pjm.2021.311.329

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.

Keywords

arithmetic dynamics, heights, random iteration

Mathematical Subject Classification

Primary: 11G50, 37A50, 37P15

Secondary: 11R32

Milestones

Received: 27 April 2020

Revised: 22 October 2020

Accepted: 14 January 2021

Published: 31 July 2021