Dynamique des nombres et physique des oscillateurs

TL;DR

This paper explores the number-theoretic structure of superheterodyning systems, revealing arithmetical rules governing their frequency spectra and introducing a new dynamical system on numbers.

Contribution

It provides a novel number-theoretic framework to predict frequency spectrum features and introduces a new dynamical system related to oscillators.

Findings

Frequency spectrum governed by arithmetical rules

Predictive framework for spectral features

Introduction of a new dynamical system on numbers

Abstract

We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system is governed by arithmetical rule. We provide a number theoritical framework which allows us to predict all the particular features of the experimental frequency spectrum. We also introduce a new natural dynamical system on numbers and study its first properties.