Y. Achdou, F. Camilli, and I. C. Dolcetta, HOMOGENIZATION OF HAMILTON???JACOBI EQUATIONS: NUMERICAL METHODS, Mathematical Models and Methods in Applied Sciences, vol.18, issue.07, pp.1115-1143, 2008.
DOI : 10.1142/S0218202508002978

O. Alvarez, Homogenization of Hamilton-Jacobi Equations in Perforated Sets, Journal of Differential Equations, vol.159, issue.2, pp.543-577, 1999.
DOI : 10.1006/jdeq.1999.3665

O. Alvarez and M. Bardi, Singular Perturbations of Nonlinear Degenerate Parabolic PDEs: a General Convergence Result, Archive for Rational Mechanics and Analysis, vol.170, issue.1, pp.17-61, 2003.
DOI : 10.1007/s00205-003-0266-5

O. Alvarez and M. Bardi, Ergodic problems in differential games In Advances in dynamic game theory, volume 9 of Ann, Internat. Soc. Dynam. Games Birkhäuser Boston, pp.131-152, 2007.

O. Alvarez and M. Bardi, Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations, Memoirs of the American Mathematical Society, vol.204, issue.960, 2010.
DOI : 10.1090/S0065-9266-09-00588-2

O. Alvarez, M. Bardi, and C. Marchi, Multiscale problems and homogenization for second-order Hamilton???Jacobi equations, Journal of Differential Equations, vol.243, issue.2, pp.349-387, 2007.
DOI : 10.1016/j.jde.2007.05.027

O. Alvarez, M. Bardi, and C. Marchi, MULTISCALE SINGULAR PERTURBATIONS AND HOMOGENIZATION OF OPTIMAL CONTROL PROBLEMS, Geometric control and nonsmooth analysis
DOI : 10.1142/9789812776075_0001

M. Arisawa and P. Lions, On ergodic stochastic control, Communications in Partial Differential Equations, vol.318, issue.11-12, pp.2187-2217, 1998.
DOI : 10.1137/0319020

M. Bardi, On differential games with long-time-average cost In Advances in dynamic games and their applications, Internat. Soc. Dynam. Games, vol.10, pp.3-18, 2009.

M. Bardi and I. C. Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations, Birkhäuser Boston Inc, 1997.
DOI : 10.1007/978-0-8176-4755-1

G. Barles, Some homogenization results for non-coercive Hamilton???Jacobi equations, Calculus of Variations and Partial Differential Equations, vol.20, issue.1, pp.449-466, 2007.
DOI : 10.1007/s00526-007-0097-6

URL : https://hal.archives-ouvertes.fr/hal-00071284

G. Barles and P. E. Souganidis, Some counterexamples on the asymptotic behavior of the solutions of Hamilton???Jacobi equations, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.330, issue.11, pp.963-968, 2000.
DOI : 10.1016/S0764-4442(00)00314-1

K. Bhattacharya and B. Craciun, Homogenization of a Hamilton-Jacobi equation associated with the geometric motion of an interface, Proc. Roy. Soc. Edinburgh Sect. A, pp.773-805, 2003.

I. Birindelli and J. Wigniolle, Homogenization of Hamilton-Jacobi equations in the Heisenberg group, Commun. Pure Appl. Anal, vol.2, issue.4, pp.461-479, 2003.

A. Braides and A. Defranceschi, Homogenization of multiple integrals, of Oxford Lecture Series in Mathematics and its Applications, 1998.

F. Camilli and A. Siconolfi, Effective Hamiltonian and Homogenization of Measurable Eikonal Equations, Archive for Rational Mechanics and Analysis, vol.56, issue.1, pp.1-20, 2007.
DOI : 10.1007/s00205-006-0001-0

I. , C. Dolcetta, and H. Ishii, On the rate of convergence in homogenization of Hamilton- Jacobi equations, Indiana Univ. Math. J, vol.50, issue.3, pp.1113-1129, 2001.

P. Cardaliaguet, Ergodicity of Hamilton???Jacobi equations with a noncoercive nonconvex Hamiltonian in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msup><mml:mi mathvariant="double-struck">R</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo stretchy="false">/</mml:mo><mml:msup><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.27, issue.3, pp.837-856, 2010.
DOI : 10.1016/j.anihpc.2009.11.015

P. Cardaliaguet, P. Lions, and P. E. Souganidis, A discussion about the homogenization of moving interfaces, Journal de Math??matiques Pures et Appliqu??es, vol.91, issue.4, pp.339-363, 2009.
DOI : 10.1016/j.matpur.2009.01.014

URL : https://hal.archives-ouvertes.fr/hal-00667312

P. Cardaliaguet, J. Nolen, and P. E. Souganidis, Homogenization and Enhancement for the G???Equation, Archive for Rational Mechanics and Analysis, vol.7, issue.1, pp.527-561, 2011.
DOI : 10.1007/s00205-010-0332-8

URL : https://hal.archives-ouvertes.fr/hal-00462050

A. Davini and A. Siconolfi, Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case, Mathematische Annalen, vol.20, issue.1, pp.749-782, 2009.
DOI : 10.1007/s00208-009-0372-2

L. C. Evans, Synopsis, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.120, issue.3-4, pp.3-4245, 1992.
DOI : 10.1090/S0002-9947-1983-0690039-8

L. C. Evans, A Survey of partial differential equations methods in weak KAM theory, Communications on Pure and Applied Mathematics, vol.1589, issue.4, pp.445-480, 2004.
DOI : 10.1002/cpa.20009

A. Fathi, Weak KAM Theorem in Lagrangian Dynamics, Lecture Notes

D. A. Gomes, Hamilton-Jacobi methods for Vakonomic Mechanics, Nonlinear Differential Equations and Applications NoDEA, vol.14, issue.3-4, pp.233-257, 2007.
DOI : 10.1007/s00030-007-5012-5

K. Horie and H. Ishii, Homogenization of Hamilton-Jacobi equations on domains with small scale periodic structure, Indiana University Mathematics Journal, vol.47, issue.3, pp.1011-1058, 1998.
DOI : 10.1512/iumj.1998.47.1385

C. Imbert and R. Monneau, Homogenization of First-Order Equations with $$(u/\varepsilon)$$ -Periodic Hamiltonians. Part I: Local Equations, Archive for Rational Mechanics and Analysis, vol.57, issue.5, pp.49-89, 2008.
DOI : 10.1007/s00205-007-0074-4

H. Ishii, Almost periodic homogenization of Hamilton-Jacobi equations, International Conference on Differential Equations, pp.600-605, 1999.
DOI : 10.1142/9789812792617_0122

C. Marchi, On the convergence of singular perturbations of Hamilton-Jacobi equations, Communications on Pure and Applied Analysis, vol.9, issue.5, pp.1363-1377, 2010.
DOI : 10.3934/cpaa.2010.9.1363

F. Rezakhanlou and J. E. Tarver, Homogenization for??Stochastic Hamilton-Jacobi Equations, Archive for Rational Mechanics and Analysis, vol.151, issue.4, pp.277-309, 2000.
DOI : 10.1007/s002050050198

P. Soravia, Pursuit???Evasion Problems and Viscosity Solutions of Isaacs Equations, SIAM Journal on Control and Optimization, vol.31, issue.3, pp.604-623, 1993.
DOI : 10.1137/0331027

P. E. Souganidis, Stochastic homogenization of Hamilton-Jacobi equations and some applications, Asymptot. Anal, vol.20, issue.1, pp.1-11, 1999.

B. Stroffolini, Homogenization of Hamilton-Jacobi equations in Carnot Groups, ESAIM: Control, Optimisation and Calculus of Variations, vol.13, issue.1, pp.107-119, 2007.
DOI : 10.1051/cocv:2007005

G. Terrone, Singular perturbation and homogenization problems in control theory, differential games and fully nonlinear partial differential equations, 2008.

C. Viterbo, Symplectic homogenization. Preprint, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00201500

J. Xin, An introduction to fronts in random media Received xxxx 20xx; revised xxxx 20xx, 2009.