Vol. 311, No. 2, 2021

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Dynamical height growth: left, right, and total orbits

Wade Hindes

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

Let S be a set of dominant rational self-maps on 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
Authors
Wade Hindes
Texas State University
San Marcos, TX
United States