Dynamics measured in a non-Archimedean field

TL;DR

This paper extends classical dynamical systems concepts like measures, entropy, and isomorphisms to a setting where measures take values in a non-Archimedean field, broadening the mathematical framework for such systems.

Contribution

It introduces a framework for analyzing dynamical systems with measures valued in non-Archimedean fields, adapting key notions from classical dynamics.

Findings

Development of non-Archimedean measure theory for dynamical systems

Translation of entropy and isomorphism concepts to non-Archimedean context

Foundation for further research in non-Archimedean dynamical systems

Abstract

We study dynamical systems using measures taking values in a non-Archimedean field. The underlying space for such measure is a zero-dimensional topological space. In this paper we elaborate on the natural translation of several notions, e.g., probability measures, isomorphic transformations, entropy, from classical dynamical systems to a non-Archimedean setting.