M. Aspenberg, The Collet-Eckmann condition for rational functions on the Riemann sphere, Mathematische Zeitschrift, vol.273, issue.3-4, pp.935-980, 2013.

M. Astorg and F. Bianchi, Bifurcations in families of polynomial skew products, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01686334

M. Astorg, L. Boc-thaler, and H. Peters, Wandering domains arising from Lavaurs maps with Siegel disks, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02177981

M. Astorg, X. Buff, R. Dujardin, H. Peters, and J. Raissy, A two-dimensional polynomial mapping with a wandering Fatou component, Annals of mathematics, vol.184, issue.1, pp.263-313, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01610414

M. Astorg and T. Gauthier, Nicolae Mihalache, and Gabriel Vigny. Collet, Eckmann and the bifurcation measure, 2017.

A. Avila and M. Lyubich, Lebesgue measure of Feigenbaum Julia sets, 2015.

A. Avila and C. G. Moreira, Statistical properties of unimodal maps: smooth families with negative schwarzian derivative, Asterisque, 2003.

A. Avila and C. G. Moreira, Statistical properties of unimodal maps, Publications Mathématiques de l'IHÉS, vol.101, pp.1-67, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00101825

L. Barreira and . Ya-b-pesin, Lyapunov exponents and smooth ergodic theory, vol.23, 2002.

L. Boc-thaler, J. E. Fornaess, and H. Peters, Fatou components with punctured limit sets. Ergodic theory and dynamical systems, vol.35, pp.1380-1393, 2015.

H. Brolin, Invariant sets under iteration of rational functions, Arkiv för matematik, vol.6, issue.2, pp.103-144, 1965.

X. Buff and A. Chéritat, Quadratic Julia sets with positive area, Annals of Mathematics, pp.673-746, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00997304

L. Carleson, W. Peter, J. Jones, . Yoccoz, and J. Julia, Bulletin of the Brazilian Mathematical Society, vol.25, issue.1, pp.1-30, 1994.

P. Collet and J. Eckmann, Positive Liapunov exponents and absolute continuity for maps of the interval, Ergodic Theory and Dynamical Systems, vol.3, issue.1, pp.13-46, 1983.

M. Denker, F. Przytycki, and M. Urba?ski, On the transfer operator for rational functions on the Riemann sphere. Ergodic Theory and Dynamical Systems, vol.16, pp.255-266, 1996.

R. Dujardin, Hénon-like mappings in C 2, American journal of mathematics, vol.126, issue.2, pp.439-472, 2004.

R. Dujardin, A non-laminar dynamical Green current, Mathematische Annalen, vol.365, issue.1-2, pp.77-91, 2016.

C. Favre and V. Guedj, Dynamique des applications rationnelles des espaces multiprojectifs, Indiana University Mathematics Journal, vol.50, issue.2, pp.881-934, 2001.

J. Graczyk and S. Smirnov, Non-uniform hyperbolicity in complex dynamics. Inventiones mathematicae, vol.175, p.335, 2009.

J. Graczyk and G. Swiatek, Harmonic measure and expansion on the boundary of the connectedness locus, Inventiones mathematicae, vol.142, issue.3, pp.605-629, 2000.

J. Graczyk and G. Swiatek, Lyapunov exponent and harmonic measure on the boundary of the connectedness locus, International Mathematics Research Notices, issue.16, pp.7357-7364, 2014.

J. Hubbard and R. Vorth, Hénon mappings in the complex domain II: Projective and inductive limits of polynomials. arXiv preprint math/9401224, 1994.

Z. Ji, Non-wandering Fatou components for strongly attracting polynomial skew products, The Journal of Geometric Analysis, pp.1-29
URL : https://hal.archives-ouvertes.fr/hal-01710467

M. Jonsson, Dynamics of polynomial skew products on C 2, Mathematische Annalen, vol.314, issue.3, pp.403-447, 1999.

A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, vol.54, 1995.

G. Levin, F. Przytycki, and W. Shen, The Lyapunov exponent of holomorphic maps. Inventiones mathematicae, vol.205, pp.363-382, 2016.

H. Li, Topological invariance of the collet-eckmann condition for one-dimensional maps, Nonlinearity, vol.30, issue.5, p.2010, 2017.

K. Lilov, Fatou theory in two dimensions, 2004.

S. Luzzatto and L. Wang, Topological invariance of generic non-uniformly expanding multimodal maps, Mathematical Research Letters, vol.13, issue.3, pp.343-357, 2006.

J. Willard and M. , Dynamics in one complex variable, vol.160, 2006.

H. Peters and J. Raissy, Fatou components of elliptic polynomial skew products. Ergodic Theory and Dynamical Systems, pp.1-13, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01610343

H. Peters and I. M. Smit, Fatou components of attracting skew-products. The Journal of Geometric Analysis, vol.28, pp.84-110, 2018.

H. Peters and L. R. Vivas, Polynomial skew-products with wandering Fatou-disks, Mathematische Zeitschrift, vol.283, issue.1-2, pp.349-366, 2016.

V. Pliss, On a conjecture due to Smale, Diff. Uravnenija, vol.8, pp.262-268, 1972.

F. Przytycki, Lyapunov characteristic exponents are nonnegative, Proceedings of the American Mathematical Society, vol.119, issue.1, pp.309-317, 1993.

F. Przytycki, Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures, Transactions of the American Mathematical Society, vol.350, issue.2, pp.717-742, 1998.

F. Przytycki and J. Rivera-letelier, Statistical properties of topological Collet-Eckmann maps, Annales Scientifiques de l'École Normale Superieure, vol.40, pp.135-178, 2007.

F. Przytycki, J. Rivera-letelier, and S. Smirnov, Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps, Inventiones mathematicae, vol.151, issue.1, pp.29-63, 2003.

F. Przytycki and S. Rohde, Porosity of Collet-Eckmann Julia sets, Fundamenta Mathematicae, vol.155, issue.2, pp.189-199, 1998.

F. Przytycki, M. Urba?ski, and A. Zdunik, Harmonic, gibbs and hausdorff measures on repellers for holomorphic maps, ii, Studia Mathematica, vol.97, issue.3, pp.189-225, 1990.

J. Raissy, Polynomial skew-products in dimension 2: Bulging and wandering Fatou components. Bollettino dell'Unione Matematica Italiana, vol.10, pp.441-450, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01610339

M. Rees, Positive measure sets of ergodic rational maps, Annales Scientifiques de l'École Normale Supérieure, vol.19, issue.3, pp.383-407, 1986.

J. Rivera, -. Letelier, and W. Shen, Statistical properties of one-dimensional maps under weak hyperbolicity assumptions, Annales Scientifiques de l'École Normale Supérieure, vol.47, pp.1027-1083, 2014.

, Stanislav Smirnov. Symbolic dynamics and Collet-Eckmann conditions. International Mathematics Research Notices, issue.7, pp.333-351, 2000.

D. Sullivan, Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou-Julia problem on wandering domains, Annals of mathematics, vol.122, issue.2, pp.401-418, 1985.

M. Tsujii, Positive Lyapunov exponents in families of one dimensional dynamical systems, Inventiones mathematicae, vol.111, issue.1, pp.113-137, 1993.

, Statistique et Modélisation (LPSM, UMR 8001