Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations

TL;DR

This paper investigates the relationship between Lyapunov exponents and Oseledets decompositions in random delay differential systems, establishing their equivalence across different functional spaces.

Contribution

It demonstrates that Lyapunov exponents are consistent across continuous and p-summable function spaces and relates their Oseledets decompositions through natural embeddings.

Findings

Lyapunov exponents are identical in both function spaces.

Oseledets decompositions are related by natural embeddings.

Results apply to systems generated by delay differential equations.

Abstract

Linear skew-product semidynamical systems generated by random systems of delay differential equations are considered, both on a space of continuous functions as~well as on a space of $p$-summable functions. The main result states that in both cases, the Lyapunov exponents are identical, and that the Oseledets decompositions are related by natural embeddings.