Lyapunov exponents of Poisson shot-noise velocity fields

We consider the Lyapunov exponents of flows generated by a class of Markovian velocity fields. The existence of the exponents is obtained for flows on a compact set, but with the most general form of the velocity field. As a particular class, we study the homogeneous and incompressible flows. In thi...

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Bibliographic Details
Published in:Stochastic processes and their applications 2001-07, Vol.94 (1), p.29-49
Main Authors: CAGLAR, Mine, CINLAR, Erhan
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Exact sciences and technology
Homogeneous
Lyapunov exponent
Mathematical analysis
Mathematics
Ordinary differential equations
Poisson shot-noise
Sciences and techniques of general use
Stationary
Stochastic flow
Stochastic flow Lyapunov exponent Poisson shot-noise Stationary Homogeneous Turbulence
Turbulence
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Summary:We consider the Lyapunov exponents of flows generated by a class of Markovian velocity fields. The existence of the exponents is obtained for flows on a compact set, but with the most general form of the velocity field. As a particular class, we study the homogeneous and incompressible flows. In this case, the exponents are nonrandom, free of the initial position of the particle path, and their sum is zero. We numerically compute the top Lyapunov exponent on R 2 for a range of parameters to conjecture that it is strictly positive.
ISSN:0304-4149
1879-209X
DOI:10.1016/S0304-4149(01)00076-X