Accueil

Romain Dujardin

  1. Dynamics of meromorphic maps with small topological degree II: Energy and invariant measure.

    Wed, 09/23/2009 - 13:19 — SomNambul
    Authors: Romain Dujardin, Jeffrey Diller, Vincent Guedj
    Subjects: Dynamical Systems
    Abstract

    We continue our study of the dynamics of meromorphic mappings with small
    topological degree on a compact K\"ahler surface $X$. Under general hypotheses
    we are able to construct a canonical invariant measure which is mixing, does
    not charge pluripolar sets and admits a natural geometric description.

  2. Wermer examples and currents.

    Mon, 08/24/2009 - 13:10 — SomNambul
    Authors: Romain Dujardin
    Subjects: Complex Variables
    Abstract

    In this paper we give the first examples of positive closed currents in
    $\mathbb{C}^2$ with continuous potentials, vanishing self-intersection, and
    which are not laminar. More precisely, they are supported on sets "without
    analytic structure". The result is mostly interesting when the potential has
    regularity close to $C^2$, because laminarity is expected to hold in that case.
    We actually construct examples which are $C^{1,\alpha}$ for all $\alpha<1$.

Math-arch

Syndicate content