4 papers
math.AP2023
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\…
math.AP2021
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\…
math.DS2016
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…
math.DS2016
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 \…