M. Astorg and F. Bianchi, Hyperbolicity and bifurcations in holomorphic families of polynomial skew products, 2018.

. Abd-+-16]-matthieu, X. Astorg, R. Buff, H. Dujardin, J. Peters et al., A twodimensional polynomial mapping with a wandering Fatou component, Ann. of Math, vol.184, pp.263-313, 2016.

M. Astorg and T. Gauthier, Nicolae Mihalache, and Gabriel Vigny. Collet, Eckmann and the bifurcation measure. Inventiones mathematicae, vol.217, pp.749-797, 2019.

G. Bassanelli and F. Berteloot, Bifurcation currents in holomorphic dynamics on, Journal für die reine und angewandte Mathematik (Crelle's Journal), issue.608, pp.201-235, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00631420

F. Berteloot and F. Bianchi, Perturbations d'exemples de Lattès et dimension de Hausdorff du lieu de bifurcation, Journal de Mathématiques Pures et Appliquées, vol.116, pp.161-173, 2018.

F. Berteloot, F. Bianchi, and C. Dupont, Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of P k . Annales scientifiques de l'ENS, vol.51, pp.215-262, 2018.

F. Berteloot, C. Dupont, and L. Molino, Normalization of bundle holomorphic contractions and applications to dynamics (normalisation de contractions holomorphes fibrées et applications en dynamique), Annales de l'institut Fourier, vol.58, issue.6, pp.2137-2168, 2008.

X. Buff and A. L. Epstein, Bifurcation measure and postcritically finite rational maps. Complex dynamics: families and friends, pp.491-512, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00666023

F. Bianchi, Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree, Mathematische Annalen, vol.373, issue.3-4, pp.901-928, 2019.

S. Biebler, Lattès maps and the interior of the bifurcation locus, Journal of Modern Dynamics, vol.15, pp.95-130, 2019.

F. Bianchi and J. Taflin, Bifurcations in the elementary Desboves family, Proceedings of the AMS, vol.145, issue.10, pp.4337-4343, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01611690

R. Dujardin and C. Favre, Distribution of rational maps with a preperiodic critical point, American Journal of Mathematics, vol.130, issue.4, pp.979-1032, 2008.

T. Dinh and N. Sibony, Dynamics in several complex variables: endomorphisms of projective spaces and polynomial-like mappings, Holomorphic dynamical systems, pp.165-294, 2010.

C. Dupont and J. Taflin, Dynamics of fibered endomorphisms of P k . to appear on Ann, Scuola Normale Sup. Pisa, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01925373

R. Dujardin, Bifurcation currents and equidistribution on parameter space, Frontiers in Complex Dynamics, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00836301

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

R. Dujardin, Non density of stability for holomorphic mappings on P k, Journal de l'École Polytechnique, vol.4, pp.813-843, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01376983

T. Gauthier, Strong bifurcation loci of full Hausdorff dimension, Ann. Sci. Éc. Norm. Sup, vol.45, issue.4, pp.947-984, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00643360

M. Jonsson, Hyperbolic dynamics of endomorphisms, 1997.

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

C. Mcmullen, Families of rational maps and iterative root-finding algorithms, Annals of mathematics, vol.125, issue.3, pp.467-493, 1987.

C. Mcmullen, The Mandelbrot set, themes and variations, pp.1-18, 2000.

F. Przytycki, Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map, Inventiones mathematicae, vol.80, issue.1, pp.161-179, 1985.

F. Przytycki, Thermodynamic formalism methods in one-dimensional real and complex dynamics, Proceedings of International Congress of Mathematicians, pp.2081-2106, 2018.

F. Przytycki and M. Urba?ski, Conformal fractals: ergodic theory methods, vol.371, 2010.

F. Przytycki and A. Zdunik, On hausdorff dimension of polynomial not totally disconnected julia sets, 2020.

J. Taflin, Blenders near polynomial product maps of C 2, Journal of the European Mathematical Society, 2017.

A. Zdunik, Parabolic orbifolds and the dimension of the maximal measure for rational maps, Inventiones mathematicae, vol.99, issue.1, pp.627-649, 1990.

, UMR CNRS 7013, 45067 Orléans Cedex 2, France E-mail address: matthieu.astorg@univ-orleans.fr CNRS