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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…
Diophantine properties of elements of SO(3)
Vadim Kaloshin, I. Rodnianski
A number alpha in R is diophantine if it is not well approximable by rationals, i.e. for some C, nu>0 and any relatively prime p, q in Z we have |alpha q -p|>C q^{-1-\vu}. It is we…
A geometric proof of the existence of Whitney stratifications
Vadim Kaloshin
A stratification of a singular set, e.g. an algebraic or analytic variety, is, roughly, a partition of it into manifolds so that these manifolds fit together "regularly". A classic…