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# Mathematical Research Letters

## Volume 26 (2019)

### Number 4

### Bounding periods of subvarieties of $(\mathbb{P}^1)^n$

Pages: 949 – 971

DOI: https://dx.doi.org/10.4310/MRL.2019.v26.n4.a1

#### Authors

#### Abstract

Using methods of $p$-adic analysis, along with the powerful result of Medvedev and Scanlon [MS14] for the classification of periodic subvarieties of $(\mathbb{P}^1)^n$, we bound the length of the orbit of a periodic subvariety $Y \subset \mathbb{P}^1)^n$ under the action of a dominant endomorphism.

Received 7 December 2017

Accepted 5 July 2018

Published 25 October 2019