53 citations · 275 across the 20 of their papers we have counts for
21 papers
Birkhoff Conjecture for nearly centrally symmetric domains
Vadim Kaloshin, Comlan Edmond Koudjinan, Ke Zhang
In this paper we prove a perturbative version of a remarkable Bialy-Mironov (Ann.Math:389-413(196), 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symm…
Gevrey regularity for the formally linearizable billiard of Treschev
Qun Wang, Ke Zhang
Treschev made the remarkable discovery that there exists formal power series describing a billiard with locally linearizable dynamics. We show that if the frequency for the linear…
The Smoothing Proximal Gradient Algorithm with Extrapolation for the Relaxation of Regularization Problem
Jie Zhang, Xinmin Yang, Gaoxi Li +1
In this paper, we consider the exact continuous relaxation model of regularization problem which was given by Bian and Chen (SIAM J. Numer. Anal 58(1): 858-883, 2020) and pro…
Uniform exponential contraction for viscous Hamilton-Jacobi equations
Konstantin Khanin, Ke Zhang, Lei Zhang
The well known phenomenon of exponential contraction for solutions to the viscous Hamilton-Jacobi equation in the space-periodic setting is based on the Markov mechanism. However,…
The essential coexistence phenomenon in Hamiltonian dynamics
Jianyu Chen, Huyi Hu, Yakov Pesin +1
We construct an example of a Hamiltonian flow on a -dimensional smooth manifold which after being restricted to an energy surface demonstrate…
Diffusion limit for a slow-fast standard map
Alex Blumenthal, Jacopo De Simoi, Ke Zhang
Consider the map , which is conjugate to the Chirikov standard map with a large parameter. The parameter value $…
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…
Thermodynamics of the Katok Map
Yakov Pesin, Samuel Senti, Ke Zhang
We effect thermodynamical formalism for the non-uniformly hyperbolic map of the two dimensional torus known as the Katok map. It is a slowdown of a linear Anosov map nea…
Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances
Vadim Kaloshin, Jianlu Zhang, Ke Zhang
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed w…
On the uniqueness of the non-minimal matter coupling in massive gravity and bigravity
Qing-Guo Huang, Raquel H. Ribeiro, Yu-Hang Xing +2
In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a non-minimal matter coupling involving both metrics generically re-introduces the Boulware--Deser (BD) ghost. A n…
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…
Thermodynamics of Towers of Hyperbolic Type
Yakov Pesin, Samuel Senti, Ke Zhang
We introduce a class of continuous maps of a compact topological space admitting inducing schemes of hyperbolic type and describe the associated tower constructions. We the…
Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation
Qing-Guo Huang, Ke-Chao Zhang, Shuang-Yong Zhou
We extend the four-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity model to a general scalar massive-tensor theory in arbitrary dimensions, coupling a dRGT massive grav…
A strong form of Arnold diffusion for two and a half degrees of freedom
Vadim Kaloshin, Ke Zhang
In the present paper we prove a strong form of Arnold diffusion. Let be the two torus and be the unit ball around the origin in . Fix . Our…
Normally hyperbolic invariant manifolds near strong double resonance
Vadim Kaloshin, Ke Zhang
In the present paper we consider a generic perturbation of a nearly integrable system of and a half degrees of freedom , with a strictly convex…
Hyperbolicity of minimizers and regularity of viscosity solutions for random Hamilton-Jacobi equations
Konstantin Khanin, Ke Zhang
We show that for a family of randomly kicked Hamilton-Jacobi equations, the unique global minimizer is hyperbolic, almost surely. Furthermore, we prove the unique forward and backw…
Arnold diffusion in arbitrary degrees of freedom and crumpled 3-dimensional normally hyperbolic invariant cylinders
Patrick Bernard, Vadim Kaloshin, Ke Zhang
In the present paper we prove a form of Arnold diffusion. The main result says that for a "generic" perturbation of a nearly integrable system of arbitrary degrees of freedom $n\ge…
Lifting Measures to Inducing Schemes
Yakov Pesin, Samuel Senti, Ke Zhang
In this paper we study the liftability property for piecewise continuous maps of compact metric spaces, which admit inducing schemes in the sense of Pesin and Senti [PS05, PS06]. W…