Characterization of SRB measures for random dynamical systems in a Banach space

This paper considers C2 random dynamical systems in a Banach space, and proves that under some mild conditions, SRB measures are characterized by invariant measures satisfying Pesin's entropy formula, in which entropy is equal to the sum of positive Lyapunov exponents of the system. This can be...

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Bibliographic Details
Published in:Journal of Differential Equations 2024-12, Vol.413, p.411-461
Main Authors: Luo, Chiyi, Zhao, Yun
Format: Article
Language:English
Subjects:
Pesin's entropy formula
Random infinite dimensional dynamical systems
SRB measure
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Summary:This paper considers C2 random dynamical systems in a Banach space, and proves that under some mild conditions, SRB measures are characterized by invariant measures satisfying Pesin's entropy formula, in which entropy is equal to the sum of positive Lyapunov exponents of the system. This can be regarded as a random version of the main result in Blumenthal and Young's paper [8].
ISSN:0022-0396
DOI:10.1016/j.jde.2024.08.067