Backward Orbit Conjecture for Latt\'es Maps

TL;DR

This paper proves a conjecture regarding the integrality of points in the backward orbit of a Lattès map over a number field, advancing understanding in arithmetic dynamics.

Contribution

It establishes the integrality conjecture for backward orbits of Lattès maps over number fields, a significant step in arithmetic dynamics.

Findings

Proves the integrality conjecture for backward orbits of Lattès maps.

Advances the understanding of arithmetic properties of dynamical systems.

Provides new insights into the distribution of integral points in backward orbits.

Abstract

For a Latt\`es map $\phi:\mathbb P^1 \to \mathbb P^1$ defined over a number field $K$, we prove a conjecture on the integrality of points in the backward orbit of $P\in \mathbb P^1(\overline K)$ under $\phi$.