On the Ergodic Theorem for non-linear wave propagation

TL;DR

This paper investigates the ergodic theorem in the context of non-linear wave propagation, linking it with spectral analysis of self-adjoint operators and path integrals, advancing understanding in mathematical physics.

Contribution

It provides a comprehensive analysis connecting ergodic theory with non-linear wave propagation and spectral characterization, extending classical results to complex systems.

Findings

Established conditions for ergodic behavior in non-linear wave systems

Linked ergodic properties with spectral measures of operators

Extended R.A.G.E. theorem to non-linear propagation contexts

Abstract

We present a complete study of the ergodic theorem for the difficult problem of non-linear wave propagations through cylindrical measures /path integrals and the famous Ruelle-Amrein-Geogerscu-Enss (R.A.G.E.) theorem on the caracterization of continuous spectrum of self-adjoint operators.