On \'Ecalle-Hakim's theorems in holomorphic dynamics

In this survey we provide detailed proofs for the results by Hakim regarding the dynamics of germs of biholomorphisms tangent to the identity of order $k+1\ge 2$ and fixing the origin.Comment: 58 pages; revised version accepted in Proceedings of "Frontiers in Complex Dynamics

Wolff-Denjoy theorems in non-smooth convex domains

We give a short proof of Wolff-Denjoy theorem for (not necessarily smooth) strictly convex domains. With similar techniques we are also able to prove a Wolff-Denjoy theorem for weakly convex domains, again without any smoothness assumption on the boundary.Comment: 13 page

Toeplitz operators and Carleson measures in strongly pseudoconvex domains

We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain D in n complex variables. In particular, we give sharp conditions on the measure ensuring that the associated Toeplitz operator maps the Bergman space A^p(D) into A^r(D) with r>p, generalizing and making more precise results by Cuckovic and McNeal. To do so, we give a geometric characterization of Carleson measures and of vanishing Carleson measures of weighted Bergman spaces in terms of the intrinsic Kobayashi geometry of the domain, generalizing to this setting results obtained by Kaptanoglu for the unit ball.Comment: 36 page

Dynamics of two-resonant biholomorphisms

International audienceIn this paper, we study the existence of basins of attraction for germs of tworesonant biholomorphisms of $\mathbb{C}^n$ fixing a point, that is germs such that the eigenvalues of the differential at the fixed point have a two dimensional family of resonances

Wolff-Denjoy theorems in nonsmooth convex domains

International audienceWe give a short proof of Wolff-Denjoy theorem for (not necessarily smooth) strictly convex domains. With similar techniques we are also able to prove a Wolff-Denjoy theorem for weakly convex domains, again without any smoothness assumption on the boundary