53 citations · 284 across the 40 of their papers we have counts for
Showing 2014 · math.DSShow all
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math.DS2014★ 8 cited
Orbits of nearly integrable systems accumulating to KAM tori
Marcel Guardia, Vadim Kaloshin
Consider a sufficiently smooth nearly integrable Hamiltonian system of two and a half degrees of freedom in action-angle coordinates \[ H_ε(φ,I,t)=H_0(I)+εH_1(φ,I,t), φ\in T^2,\ I\…
math.DS2014
An integrable deformation of an ellipse of small eccentricity is an ellipse
Artur Avila, Jacopo De Simoi, Vadim Kaloshin
The classical Birkhoff conjecture says that the only integrable convex domains are circles and ellipses. In the paper we show that this a version of this conjecture is true for sma…
math.DS2014★ 9 cited
Dynamics of the dominant Hamiltonian, with applications to Arnold diffusion
Vadim Kaloshin, Ke Zhang
It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associat…