Statistical topography and Lyapunov exponents in stochastic dynamical systems
V.I. Klyatskin
A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation
This article discusses the relationship between the
statistical description of stochastic dynamical systems based
on the ideas of statistical topography and the traditional analysis of Lyapunov stability of dynamical systems with the use of
the Lyapunov characteristic indices (Lyapunov exponents). As
an illustration, some coherent phenomena are considered that
occur with a probability of unity, i.e., in almost all realizations
of the stochastic systems. Among such phenomena are the
diffusion and clustering of a passive tracer in random hydrodynamic flows, the dynamic localization of plane waves in
layered random media, and the emergence of caustic patterns
of the wave field in multidimensional random media.
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