ABSTRACT:

We study the existence of correctors and approximate correctors for the homogenization of Hamilton-Jacobi equations with stationary ergodic hamiltonian. As it is well known, this setting encompass the periodic and quasi periodic case. We perform a qualitative analysis of the corresponding cell problem, which generalize the one developped in the periodic case. We find representation formulae for exact and approximate correctors and propose a definition of Aubry set, suitably adapted to this framework.