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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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.1807.02680 |