Shearing in the space of adelic lattices

TL;DR

This paper explores the connection between continued fractions, number theory, and dynamics, focusing on shearing phenomena in the space of adelic lattices, with detailed explanations and proofs.

Contribution

It introduces a novel perspective linking continued fractions to shearing in adelic lattice spaces, expanding understanding of dynamical phenomena in number theory.

Findings

Identification of shearing phenomena in adelic lattices

Connection between continued fractions and adelic dynamics

Detailed proofs of the proposed concepts

Abstract

In this notes we show how a problem regarding continued fractions of rational numbers, lead to several phenomena in number theory and dynamics, and eventually to the problem of shearing of divergent diagonal orbits in the space of adelic lattices. Finding these ideas quite interesting, the first half of these notes is about explaining theses ideas, the intuition and motivation behind them, and the second contains the details and proofs.