Ergodicity of Hamilton-Jacobi equations with a non coercive non convex Hamiltonian in $\R^2/\Z^2$
Résumé
The paper investigates the long time average of the solutions of Hamilton-Jacobi equations with a non coercive, non convex Hamiltonian in the torus $\R^2/\Z^2$. We give nonresonnance conditions under which the long-time average converges to a constant. In the resonnant case, we show that the limit still exists, although it is non constant in general. We compute the limit at points where it is not locally constant.
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