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

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Dedicated to Professor Tomás Caraballo on occasion of his Sixtieth Birthday

The first author is supported by the NCN grant Maestro 2013/08/A/ST1/00275 and the last two authors are partly supported by MICIIN/FEDER under project RTI2018-096523-B-100 and EU Marie-Skłodowska-Curie ITN Critical Transitions in Complex Systems (H2020-MSCA-ITN-2014 643073 CRITICS)

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  • 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.

    Mathematics Subject Classification: Primary: 37H15, 37L55, 34K06.Secondary: 37A30, 60H25.

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