On sparsity of integral points in orbits and correspondences with big pullbacks under iterates

TL;DR

This paper establishes new unconditional results demonstrating the sparsity of integral points in orbits under various maps and correspondences across multiple dimensions, utilizing advanced diophantine approximation techniques.

Contribution

It generalizes previous theorems by Yasufuku and others, introducing novel diophantine approximation tools and recent correspondence constructions to study integral points.

Findings

Proves sparsity of integral points in orbits for many maps

Extends results to arbitrary dimensions

Utilizes new diophantine approximation methods

Abstract

We prove new unconditional results of sparsity of integral points on orbits under many maps and correspondences in arbitrary dimensions, generalizing theorems of Yasufuku(2015) and others. The main ingredients are new diophantine approximation tools and recent constructions for correspondences due to Ingram (2011).