Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces Jeremy Blanc 37F1032H5014J5014E07dynamical degreepseudo-automorphismscubics We give a way to construct groups of pseudo-au\-to\-mor\-phisms of rational varieties of any dimension that fix pointwise the image of a cubic hypersurface of $\mathbb{P}^n$. These groups are free products of involutions, and most of their elements have dynamical degree $>1$. Moreover, the Picard group of the varieties obtained is not big, if the dimension is at least $3$. We also answer a question of E. Bedford on the existence of birational maps of the plane that cannot be lifted to automorphisms of dynamical degree $>1$, even if we compose them with an automorphism of the plane. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.5040 10.1512/iumj.2013.62.5040 en Indiana Univ. Math. J. 62 (2013) 1143 - 1164 state-of-the-art mathematics http://iumj.org/access/