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



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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