Non-uniformly expanding maps with additive noise and a fully-positive-Lyapunov stationary measure are asserted to have dense random horseshoes, a random version of Smale's horseshoe.
Full-horseshoes for the Galerkin truncations of 2D Navier-Stokes equation with degenerate stochastic forcing
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In this paper, we mainly study the turbulence of Galerkin truncations of 2D Navier-Stokes equation under degenerate stochastic forcing and large-scale. We use a kind of chaotic structure named full-horseshoes to describe it. It is proved that if the stochastic forcing satisfies some kind of hypoelliptic condition, then the system has full-horseshoes.
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Non uniform expansion and additive noise imply random horseshoe
Non-uniformly expanding maps with additive noise and a fully-positive-Lyapunov stationary measure are asserted to have dense random horseshoes, a random version of Smale's horseshoe.