A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems.
A first-order canonical set of generalized Jacobi-type variables for hyperbolic orbital motion.
A new geometrical framework for time-dependent Hamiltonian mechanics.
A new method for measuring the splitting of invariant manifolds
A note on the rotationally symmetric SO(4) Euler rigid body.
A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
Algebro-geometric Integration in Classical and Statistical Mechanics
Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group
We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like where h is the mesh step. Such...