53 citations · 284 across the 40 of their papers we have counts for
4 papers · 1 filter
Density of convex billiards with rational caustics
Vadim Kaloshin, Ke Zhang
We show that in the space of all convex billiard boundaries, the set of boundaries with rational caustics is dense. More precisely, the set of billiard boundaries with caustics of…
Random Iteration of Cylinder Maps and diffusive behavior away from resonances
Oriol Castejón, Marcel Guardia, Vadim Kaloshin
In this paper we propose a model of random compositions of cylinder maps, which in the simplified form is as follows: let and \[ f_{\…
Nearly circular domains which are integrable close to the boundary are ellipses
Guan Huang, Vadim Kaloshin, Alfonso Sorrentino
The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrabi…
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
Patrick Bernard, K Kaloshin, K Zhang
We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + H1(, p, t), T n , p B n , t T = R/T be a nearly integrable system of arbitr…