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9 papers
A limit shape theorem for periodic stochastic dispersion
Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov
We consider the evolution of a connected set on the plane carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most…
Hausdorff dimension in stochastic dispersion
Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov
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…
Around Hilbert-Arnold Problem
Vadim Kaloshin
This lectures notes consists of four lectures. The first lecture discusses questions around Hilbert-Arnold Problem which is naturally arises from Quantitative Hilbert 16-th problem…
Sample path properties of the stochastic flows
Dmitry Dolgopyat, Vadim Kaloshin, Leonid Koralov
We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as th…
A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms
Vadim Yu. Kaloshin, Brian Hunt
Let M be a compact manifold of dimension at least 2, Diff^r(M) be the space of C^r diffeomorphisms of M. Define for any diffeomorphism f in Diff^r(M) number of isolated periodic po…
The Hilbert 16-th problem and an estimate for cyclicity of an elementary polycycle
Vadim Kaloshin
Hilbert-Arnold (HA) problem, motivated by Hilbert 16-th problem, is to prove that for a generic k-parameter family of smooth vector fields {\dot x=v(x,\eps)}_{\eps\in B^k} on the 2…