Probabilistic and asymptotic methods with the Perron Frobenius's operator

TL;DR

This paper presents new probabilistic and asymptotic techniques using Perron-Frobenius operators to analyze the long-term behavior of iterative processes, with applications to complex PDEs like Lorenz and Navier-Stokes.

Contribution

It introduces a comprehensive global framework for asymptotic analysis with improvements over previous work, applying these methods to complex PDEs and exploring new phenomena like resonance.

Findings

New methods for asymptotic analysis of PDEs such as Lorenz and Navier-Stokes

Enhanced understanding of the resonance phenomena in iterative systems

Refined results with corrections to earlier preprints

Abstract

We give a new global presentation of our results on the asymptotic behavior of an iteration. This paper brings many improvements and corrections to our previous preprints on the subject. Among the applications, we use new methods to compute asymptotic results of PDE like Lorenz or Navier-Stokes equations. New questions as the resonance are studied.