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math.DS2000★ 2 cited
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…
math.DS2000★ 3 cited
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…