F. José, C. Alves, M. Bonatti, and . Viana, SRB measures for partially hyperbolic systems whose central direction is mostly expanding, Invent. Math, vol.140, issue.2, pp.351-398, 2000.

F. José, C. L. Alves, S. Dias, V. Luzzatto, and . Pinheiro, SRB measures for partially hyperbolic systems whose central direction is weakly expanding, J. Eur. Math. Soc. (JEMS), vol.19, issue.10, pp.2911-2946, 2017.

V. Araújo, S. Galatolo, and M. Pacifico, Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors, Math. Z, vol.276, issue.3-4, pp.1001-1048, 2004.

A. Avila, S. Gouëzel, and J. Yoccoz, Exponential mixing for the Teichmüller flow, Publ. Math. Inst. Hautes Études Sci, vol.104, issue.1, pp.143-211, 2006.

F. José and . Alves, SRB measures for partially hyperbolic attractors, 2015.

V. Araújo, I. Melbourne, and P. Varandas, Rapid mixing for the Lorenz attractor and statistical limit laws for their time-1 maps, Comm. Math. Phys, vol.340, issue.3, pp.901-938, 2015.

V. Araujo, M. J. Pacifico, E. R. Pujals, and M. Viana, Singular-hyperbolic attractors are chaotic, Trans. Amer. Math. Soc, vol.361, issue.5, pp.2431-2485, 2009.

F. Abdenur and M. Viana, Flavors of partial hyperbolicity, vol.1, p.12, 2009.

O. Butterley and I. Melbourne, Disintegration of invariant measures for hyperbolic skew products, Israel J. Math, vol.219, issue.1, pp.171-188

R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, vol.470, 2008.

C. Cuny, . Dedecker, F. Korepanov, and . Merlevède, Rates in almost sure invariance principle for slowly mixing dynamical systems, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01688705

E. Catsigeras and H. Enrich, SRB-like measures for 0 dynamics, Bull. Pol. Acad. Sci. Math, vol.59, issue.2, pp.151-164, 2011.

A. Castro and T. Nascimento, Statistical properties of the maximal entropy measure for partially hyperbolic attractors, Ergodic Theory Dynam. Systems, vol.37, issue.4, pp.1060-1101, 2002.

S. Crovisier and R. Potrie, Introduction to partially hyperbolic dynamics, School on Dynamical Systems, ICTP, vol.3, issue.1, 2015.

V. Climenhaga, Y. Pesin, and A. Zelerowicz, Equilibrium states in dynamical systems via geometric measure theory, 2018.

T. James, A. N. Campbell, and . Quas, A generic 1 expanding map has a singular S-R-B measure, Comm. Math. Phys, vol.221, issue.2, pp.335-349, 2001.

A. Castro and P. Varandas, Equilibrium states for non-uniformly expanding maps: decay of correlations and strong stability, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.30, issue.2, pp.225-249, 2002.

L. J. Díaz, V. Horita, I. Rios, and M. Sambarino, Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes. Ergodic Theory Dynam, Systems, vol.29, issue.2, pp.433-474, 2009.

A. Fan and Y. Jiang, On Ruelle-Perron-Frobenius operators. I. Ruelle theorem, Comm. Math. Phys, vol.223, issue.1, pp.125-141, 2001.

A. Fan and Y. Jiang, On Ruelle-Perron-Frobenius operators. II. Convergence speeds, Comm. Math. Phys, vol.223, issue.1, pp.143-159, 2001.

S. Galatolo, Quantitative statistical stability and speed of convergence to equilibrium for partially hyperbolic skew products, J. Éc. polytech. Math, vol.5, pp.377-405, 2018.

S. Galatolo and R. Lucena, Spectral gap and quantitative statistical stability for systems with contracting fibers and lorenz like maps, 2004.

S. Galatolo, I. Nisoli, and M. J. Pacifico, Decay of correlations, quantitative recurrence and logarithm law for contracting lorenz attractors, Journal of Statistical Physics, vol.170, issue.5, pp.862-882, 2018.

S. Gouëzel, Almost Sure Invariance Principle for dynamical systems by spectral methods. The Annals of Probability, vol.38, pp.1639-1671, 2010.

S. Galatolo and M. Pacifico, Lorenz-like flows: exponential decay of correlations for the Poincaré map, logarithm law, quantitative recurrence. Ergodic Theory Dynam. Systems, vol.30, pp.1703-1737, 2004.

P. Guihéneuf, Dynamical properties of spatial discretizations of a generic homeomorphism, Ergodic Theory Dynam. Systems, vol.35, issue.5, pp.1474-1523, 2015.

B. Kloeckner, An optimal transportation approach to the decay of correlations for non-uniformly expanding maps. Ergodic Theory Dynam. Systems, vol.1, p.7, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01626239

K. Kuratowski and C. Ryll-nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys, vol.13, issue.5, pp.397-403, 1965.

F. Ledrappier, Principe variationnel et systemes dynamiques symboliques. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.30, pp.185-202, 1974.

F. Ledrappier, Propriétés ergodiques des mesures de sinai. Publications Mathématiques de l'Institut des Hautes Études Scientifiques, vol.59, p.12, 1984.

R. Leplaideur, K. Oliveira, and I. Rios, Equilibrium states for partially hyperbolic horseshoes. Ergodic Theory Dynam, Systems, vol.31, issue.1, pp.179-195, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00202571

F. Ledrappier and P. Walters, A relativised variational principle for continuous transformations, J. London Math. Soc, vol.16, issue.2, pp.568-576, 1977.

I. Melbourne and M. Nicol, Almost sure invariance principle for nonuniformly hyperbolic systems, Comm. Math. Phys, vol.260, issue.1, pp.131-146, 2005.

I. Melbourne and A. Török, Central Limit Theorems and Invariance Principles for time-one maps of hyperbolic flows, Communications in Mathematical Physics, vol.229, issue.1, pp.57-71, 2002.

V. A. Rohlin, On the fundamental ideas of measure theory, pp.55-1952

V. Ramos and J. Siqueira, On equilibrium states for partially hyperbolic horseshoes: uniqueness and statistical properties, Bull. Braz. Math. Soc. (N.S.), vol.48, issue.3, pp.347-375, 2017.

D. Simmons, Conditional measures and conditional expectation

, Rohlin's disintegration theorem, Discrete Contin. Dyn. Syst, vol.32, issue.7, pp.2565-2582, 2012.

S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc, vol.73, issue.7, pp.747-817, 1967.

M. Thaler, Estimates of the invariant densities of endomorphisms with indifferent fixed points, Israel J. Math, vol.37, issue.4, pp.303-314, 1980.

M. Tyran-kami?ska, An invariance principle for maps with polynomial decay of correlations, Comm. Math. Phys, vol.260, issue.1, pp.1-15, 2005.

C. Villani, Optimal transport, of Grundlehren der Mathematischen Wissenschaften, vol.338
URL : https://hal.archives-ouvertes.fr/hal-00974770

. Springer-verlag, , 2009.

P. Walters, Ruelle's operator theorem and -measures, Trans. Amer. Math. Soc, vol.214, issue.7, pp.375-387, 1975.

P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, vol.79, issue.1, 1982.

L. Young, Statistical properties of dynamical systems with some hyperbolicity, Ann. of Math, vol.147, issue.2, pp.585-650, 1998.

L. Young, What are SRB measures, and which dynamical systems have them, Journal of Statistical Physics, vol.108, issue.5-6, pp.733-754, 2002.