6 papers
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…
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…
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…