Viet-Anh Nguyen

Comparison of dynamical degrees for semi-conjugate meromorphic maps

Let f be a dominant meromorphic self-map on a projective manifold X which preserves a meromorphic fibration pi: X --> Y of X over a projective manifold Y. We establish formulas relating the dynamical degrees of f, the dynamical degrees of f relative to the fibration and the dynamical degrees of the self-map g on Y induced by f. Applications are given.

ON THE DYNAMICAL DEGREES OF MEROMORPHIC MAPS PRESERVING A FIBRATION

Let f be a dominant meromorphic self-map on a compact Kahler manifold X which preserves a meromorphic fibration π : X → Y of X over a compact Kahler manifold Y. We compute the dynamical degrees of f in terms of its dynamical degrees relative to the fibration and the dynamical degrees of the map g : Y → Y induced by f. We derive from this result new properties of some fibrations intrinsically associated to X when this manifold admits an interesting dynamical system.

Growth of the number of periodic points for meromorphic maps

We show that any dominant meromorphic self-map f:X→X of a compact Kahler manifold X is an Artin–Mazur map. More precisely, if Pn(f) is the number of its isolated periodic points of period n (counted with multiplicity), then Pn(f) grows at most exponentially fast with respect to n and the exponential rate is at most equal to the algebraic entropy of f. Further estimates are given when X is a surface. Among the techniques introduced in this paper, the h-dimension of the density between two arbitrary positive closed currents on a compact Kahler surface is obtained.

Geometric Characterization of Lyapunov Exponents for Riemann Surface Laminations

We characterize geometrically the Lyapunov exponents of a cocycle (of arbitrary rank) with respect to a harmonic current defined on a hyperbolic Riemann surface lamination. Our characterizations are formulated in terms of the expansion rates of the cocycle along geodesic rays.

Singular holomorphic foliations by curves I: integrability of holonomy cocycle in dimension 2

We study the holonomy cocycle

Approximation and equidistribution results for pseudo-effective line bundles

\mathcal H

Exponential estimates for plurisubharmonic functions

H of a holomorphic foliation