J. Aaronson, H. Nakada, O. Sarig, and R. Solomyak, Invariant measures and asymptotics for some skew products, Israël Journal of Math, vol.128, pp.93-134, 2002.

V. I. Arnold, Small denominators I. Mapping the circle onto itself, Russian) Izv. Akad. Nauk SSSR Ser. Mat, vol.25, pp.21-86, 1961.

J. Brémont, On planar random walks in environments invariant by horizontal translations, Markov Processes and Related Fields, vol.22, pp.267-310, 2016.

J. Brémont, Markov chains in a stratified environment, ALEA, Lat. Am. J. Probab. Math. Stat, vol.14, pp.751-798, 2017.

J. Brémont, Random walk in a stratified independent random environment, Electronic Communications In Probability, vol.24, pp.1-15, 2019.

M. Campanino and D. Petritis, Random walks on randomly oriented lattices, Markov Processes and Related Fields, vol.9, pp.391-412, 2003.

M. Campanino and D. Petritis, Type transitions of simple random walks on randomly directed regular lattices, Journal of Applied Probability, vol.51, pp.1065-1080, 2014.

J. Conze and Y. , Guivarc'h, Marches en milieu aléatoire et mesures quasi-invariantes pour un système dynamique, Colloquium Mathematicum v. 84/85, pp.457-480, 2000.

J. Conze and J. Marco, Remarks on step cocycles over rotations, centralizers and coboundaries, Ergodic theory and dynamical systems, pp.93-115, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00787624

A. Devulder and F. Pene, Random walk in random environment in a two-dimensional stratified medium with orientations, Electron. Journal of Probab, vol.18, issue.88, pp.1-23, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00634636

D. Dolgopyat and O. Sarig, Quenched and annealed temporal limit theorems for circle rotations, Asterisque, vol.415, pp.57-83, 2020.

N. Guillotin-plantard and A. L. Ny, Transient random walks on 2D-oriented lattices, vol.52, pp.699-711, 2008.

A. Khinchin and M. Kettenbruchprobleme, Compositio Math, vol.1, pp.361-382, 1935.

A. Khinchin, Continued fractions, 1997.

D. H. Kim and S. Marmi, The recurrence time for interval exchange maps, Nonlinearity, vol.21, pp.2201-2210, 2008.

M. Matheron and G. De-marsily, Is transport in porous media always diffusive ? A counterexample, Water resources Res, vol.16, pp.901-907, 1980.

F. Pene, Transient random walk in Z 2 with stationary orientations, ESAIM Probability and Statistics, vol.13, pp.417-436, 2009.

, Faculté des Sciences et Technologies, 61, avenue du Général de Gaulle, 94010 Créteil Cedex