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

Janusz Mierczyński; Sylvia Novo; Rafael Obaya

doi:10.3934/cpaa.2020098

Article Contents

2020, Volume 19, Issue 4: 2235-2255. Doi: 10.3934/cpaa.2020098

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

1.
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, PL-50-370 Wrocław, Poland
2.
Departamento de Matemática Aplicada, E.I. Industriales, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid, Spain

Dedicated to Professor Tomás Caraballo on occasion of his Sixtieth Birthday

Received: August 31, 2018

Revised: September 30, 2019

Published: January 2020

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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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.

Keywords:

Random dynamical systems,
linear systems of delay differential equations,
Lyapunov exponents,
Oseledets decomposition.

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

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