Hausdorff Dimension in Stochastic Dispersion
Copyright policy )Hausdorff Dimension in Stochastic Dispersion
We consider the evolution of a connected set in Euclidean space carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order sqrt{t} away from the origin [DKK1], there is an uncountable set of measure zero of points, which escape to infinity at the linear rate [CSS1]. In this paper we prove that this set of linear escape points has full Hausdorff dimension.
26 pages
- Massachusetts Institute of Technology United States
- Pennsylvania State University United States
- College of New Jersey United States
- Penza State University Russian Federation
Dimension theory of smooth dynamical systems, Probability (math.PR), Lyapunov exponents, Hausdorff dimension, Dynamical Systems (math.DS), Stochastic ordinary differential equations (aspects of stochastic analysis), Dynamical systems and their relations with probability theory and stochastic processes, Fractals, Classical dynamic and nonequilibrium statistical mechanics (general), Stochastic flows, FOS: Mathematics, Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.), Mathematics - Dynamical Systems, Mathematics - Probability
Dimension theory of smooth dynamical systems, Probability (math.PR), Lyapunov exponents, Hausdorff dimension, Dynamical Systems (math.DS), Stochastic ordinary differential equations (aspects of stochastic analysis), Dynamical systems and their relations with probability theory and stochastic processes, Fractals, Classical dynamic and nonequilibrium statistical mechanics (general), Stochastic flows, FOS: Mathematics, Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.), Mathematics - Dynamical Systems, Mathematics - Probability
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