16 citations · 64 across the 21 of their papers we have counts for
21 papers
Generalized convergence of solutions for nonlinear Hamilton-Jacobi equations with state-constraint
Son Tu, Jianlu Zhang
For a continuous Hamiltonian , we consider the asymptotic behavior of associated Hamilton--Jacobi equatio…
Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: The central role of Mather measures
Qinbo Chen, Albert Fathi, Maxime Zavidovique +1
Given a continuous Hamiltonian defined on , where is a closed connected manifold, we study viscosity solutions, $u_λ: M\…
On the negative limit of viscosity solutions for discounted Hamilton-Jacobi equations
Ya-Nan Wang, Jun Yan, Jianlu Zhang
Suppose is a closed Riemannian manifold. For a generic (in the sense of Mañé) Tonelli Hamiltonian , the minimal viscosity solution $u_λ^-:M\…
Parameterized viscosity solutions of convex Hamiltonian systems with time periodic damping
Ya-Nan Wang, Jun Yan, Jianlu Zhang
In this article we develop an analogue of Aubry Mather theory for time periodic dissipative equation \[ \left\{ \begin{aligned} \dot x&=\partial_p H(x,p,t),\\ \dot p&=-\partial_x H…
Essential forward weak KAM solution for the convex Hamilton-Jacobi equation
Xifeng Su, Jianlu Zhang
For a convex, coercive continuous Hamiltonian on a compact closed Riemannian manifold , we construct a unique forward weak KAM solution of \[ H(x, d_x u)=c(H) \] by a vanishing…
Spectral invariants of convex billiard maps:a viewpoint of Mather's beta function
Jianlu Zhang
For strictly convex billiard maps of smooth boundaries, we get a Birkhoff normal form via a list of constructive generating functions. Based on this, we get an explicit formula for…
Variational attraction of the KAM torus for the conformally symplectic system
Liang Jin, Jianlu Zhang, Kai Zhao
For the conformally symplectic system \[ \left\{ \begin{aligned} \dot{q}&=H_p(q,p),\quad(q,p)\in T^*\mathbb{T}^n\\ \dot p&=-H_q(q,p)-λp, \quad λ>0 \end{aligned} \right. \] with a p…
Smooth subsolutions of the discounted Hamilton-Jacobi equations
Xiyao Huang, Liang Jin, Jianlu Zhang +1
For the discounted Hamilton-Jacobi equation,we construct subsolutions which are indeed solutions on the projected Aubry set. The smoothnes…
Global Behaviors of weak KAM Solutions for exact symplectic Twist Maps
Jianlu Zhang
We investigated several global behaviors of the weak KAM solutions parametrized by . For the suspended Hamiltonian of the exact…
Convergence of viscosity solutions of generalized contact Hamilton-Jacobi equations
Yanan Wang, Jun Yan, Jianlu Zhang
For any compact connected manifold , we consider the generalized contact Hamiltonian defined on which is conex in and monotonically increasi…
Oscillatory orbits in the Restricted Planar 4 Body Problem
Tere Seara, Jianlu Zhang
The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), of which the motion g…
Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem
Marcel Guardia Vadim Kaloshin, Jianlu Zhang
For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set in phase space independent of fixed measure, where the set of initial points w…
Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps
Vadim Kaloshin, Jianlu Zhang
For symmetrically analytic deformation of the circle (with certain Fourier decaying rate), the necessary condition for the corresponding billiard map to keep the coexistence of per…
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…
Generically Mane set supports uniquely ergodic measure for residual cohomology class
Jianlu Zhang
In this paper, we proved that for generic Tonelli Lagrangian, there always exists a residual set such that \[ \widetilde{\mathcal{M}}(c)=\wid…
Suspension of the Billiard maps in the Lazutkin's coordinate
Jianlu Zhang
In this paper we proved that under the Lazutkin's coordinate, the billiard map can be interpolated by a time-1 flow of a Hamiltonian which can be formally expressed by \…
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…
A second order expansion of the separatrix map for trigonometric perturbations of a priori unstable systems
M. Guardia, V. Kaloshin, J. Zhang
In this paper we study a so-called separatrix map introduced by Zaslaskii-Filonenko [ZF68] and studied by Treschev and Piftankin [Tre98, Tre02, Pif06, PT07]. We derive a second ord…
Asymptotic trajectories of KAM torus
Jianlu Zhang, Chong-Qing Cheng
In this paper we construct a certain type of nearly integrable systems of two and a half degrees of freedom: \[H(p,q,t)=h(p)+εf(p,q,t),\quad (q,p)\in T^{*}\mathbb{T}^2,t\in \mathbb…
Optimal Transportation for Generalized Lagrangian
Ji Li, Jianlu Zhang
In this paper, we study the optimal transportation for generalized Lagrangian , and consider the cost function as following: $$c(x, y)=\inf_{\substack{x(0)=x\\x(1)=y\\…
Non-differentiability of Alpha function at the boundary of flat
Zhang Jianlu
With the variational method introduced by J Mather, we construct a mechanical Hamiltonian system whose Alpha function has a flat F and is non-differentiable at the boundary of F. I…