$C^m-$ linearization of discrete random dynamical systems

TL;DR

This paper proves that certain discrete random dynamical systems can be smoothly transformed into their linear counterparts, extending classical results to more general, nonautonomous, and stochastic settings.

Contribution

It generalizes $C^m$ linearization results from deterministic to discrete random dynamical systems under broad assumptions.

Findings

Established $C^m$ topological equivalence for nonautonomous semilinear difference equations.

Extended linearization results to discrete random dynamical systems.

Provided conditions for both global and local linearization.

Abstract

This paper establishes $C^m$ topological equivalence of nonautonomous semilinear difference equation with its linearization and generalizes the obtained results to discrete random dynamical systems, considering both, global and local, assumptions.