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We try to find a geometric interpretation of the wedge product of positive closed laminar currents in C2. We say such a wedge product is geometric if it is given by intersecting the disks filling up the currents. Uniformly laminar currents do always intersect geometrically in this sense. We also introduce a class of strongly approximable laminar currents, natural from the dynamical point of view, and prove that such currents intersect geometrically provided they have continuous potentials.

Let ${\left(f_{\lambda }\right)}_{\lambda \in \Lambda }$ be a holomorphic family of rational mappings of degree $d$ on ${\mathbb{P}}^1\left(ℂ\right)$, with $k$ marked critical points $c_1,...,c_k$. To this data is associated a closed positive current $T_1\wedge \cdots \wedge T_k$ of bidegree $(k,k)$ on $\Lambda$, aiming to describe the simultaneous bifurcations of the marked critical points. In this note we show that the support of this current is accumulated by parameters at which $c_1,...,c_k$ eventually fall on repelling cycles. Together with results of Buff, Epstein and Gauthier, this leads to a complete characterization of $\mathrm{Supp}(T_1\wedge \cdots \wedge T_k)$.

We continue our study of the dynamics of mappings with small topological degree on projective complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic “equilibrium” measure for each such mapping. Here we study the dynamical properties of this measure in detail: we give optimal bounds for its Lyapunov exponents, prove that it has maximal entropy, and show that it has product structure in the natural extension. Under a natural further assumption, we show that saddle points...