From configurations to branched configurations and beyond

TL;DR

This paper introduces a geometric and topological framework to analyze branching phenomena across fields like statistical mechanics and turbulence, aiming to understand these effects more comprehensively.

Contribution

It develops a novel geometric-topological setting for studying branching effects and explores limits within dynamical systems on probability spaces.

Findings

New framework for branching effects in physics and mathematics

Limit constructions in dynamical systems on probability spaces

Potential for comprehensive analysis of branching phenomena

Abstract

We propose here a geometric and topological setting for the study of branching effects arising in various fields of research, e.g. in statistical mechanics and turbulence theory. We describe various aspects that appear key points to us, and finish with a limit of such a construction which stand in the dynamics on probability spaces where it seems that branching effects can be fully studied without any adaptation of the framework.