Chaos and Non-Archimedean metric in the Bernoulli map

TL;DR

This paper applies ultrametric and non-Archimedean metrics to analyze the chaotic properties of the Bernoulli map, offering simpler explanations for Lyapunov exponents and entropy through p-adic time concepts.

Contribution

It introduces ultrametric and non-Archimedean metrics as effective tools for understanding chaos in the Bernoulli map, highlighting the natural emergence of p-adic time.

Findings

Non-Archimedean metrics effectively describe chaos in the Bernoulli map.

Lyapunov exponent and Kolmogorov entropy are explained via ultrametric properties.

p-adic time arises naturally from ultrametric analysis.

Abstract

Ultrametric concepts are applied to the Bernoulli map, showing the adequateness of the non-Archimedean metrics to describe in a simple and direct way the chaotic properties of this map. Lyapunov exponent and Kolmogorov entropy appear to find a simpler explanation. A p-adic time emerges as a natural consequence of the ultrametric properties of the map.