Lyapunov Spectrum of Nonautonomous Linear Young Differential Equations

We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is independent of the driving path for triangular systems which are...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2020-12, Vol.32 (4), p.1749-1777
Main Authors: Cong, Nguyen Dinh, Duc, Luu Hoang, Hong, Phan Thanh
Format: Article
Language:English
Subjects:
Applications of Mathematics
Chaos theory
Differential equations
Liapunov exponents
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Parameters
Partial Differential Equations
Random variables
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Summary:We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is independent of the driving path for triangular systems which are regular in the sense of Lyapunov. In the stochastic setting, the system generates a stochastic two-parameter flow which satisfies the integrability condition, hence the Lyapunov exponents are random variables of finite moments. Finally, we prove a Millionshchikov theorem stating that almost all, in a sense of an invariant measure, linear nonautonomous Young differential equations are Lyapunov regular.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-019-09780-z