53 citations · 275 across the 20 of their papers we have counts for
4 papers · 2 filters
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…
Exponential convergence of solutions for random Hamilton-Jacobi equations
Renato Iturriaga, Konstantin Khanin, Ke Zhang
We show that for a family of randomly kicked Hamiton-Jacobi equations on the torus, almost surely, the solution of an initial value problem converges exponentially fast to the uniq…
Improved stability for analytic quasi-convex nearly integrable systems and optimal speed of Arnold diffusion
Jianlu Zhang, Ke Zhang
We improve the global Nekhoroshev stability for analytic quasi-convex nearly integrable Hamiltonian systems. The new stability result is optimal, as it matches the fastest speed of…
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…