arXiv subjects

Nessim Sibony

Publications and source records attributed to Nessim Sibony.

41 records · Page 3Linked to original sources

arXiv2004

Regularization of currents and entropy

Let T be a positive closed (p,p)-current of mass 1 on a compact Kahler manifold X. Then, there exist a constant c, independent of T, and smooth positive closed (p,p)-currents Tn and Sn of mass c such that Tn-Sn converge weakly to T. We also extend this result to positive pluriharmonic currents. Then we study the wedge product of positive closed (1,1)-currents having continuous potential with positive pluriharmonic currents. As an application, we give an estimate of the topological entropy of meromorphic maps on compact Kahler manifolds.

math.CV↗

arXiv2004

Decay of correlations and central limit theorem for meromorphic maps

Let f be a dominating meromorphic self-map of large topological degree on a compact Kaehler manifold. We give a new construction of the equilibrium measure of f and prove that it is exponentially mixing. Then, we deduce the central limit theorem for Lipschitzian observables.

math.DS↗

arXiv2004

On the dynamics near infinity of some polynomial mappings in $\mathbb{C}^2$

We construct the Green current for a random iteration of "horizontal-like" mappings in two complex dimensions. This is applied to the study of a polynomial map $f:\mathbb{C}^2\to\mathbb{C}^2$ with the following properties: 1. infinity is $f$-attracting, 2. $f$ contracts the line at infinity to a point not in the indeterminacy set. Then the Green current of $f$ can be decomposed into pieces associated with an itinerary determined by the indeterminacy points. We also study the set of escape rates near infinity, i.e. the possible values of the function $\limsup \frac{1}{n}\log^+\log^+ \norm{f^n}$. We exhibit examples for which this set contains an interval.

math.DS↗

arXiv2004

Harmonic Currents of Finite Energy and Laminations

We introduce, on a complex Kahler manifold (M,ω), a notion of energy for harmonic currents of bidegree (1,1). This allows us to define $\int T \wedge T \wedge ω^{k-2},$ for positive harmonic currents. We then show that for a lamination with singularities of a compact set in P^2 there is a unique positive harmonic current which minimizes energy. If X is a compact laminated set in P^2 of class C^1 it carries a unique positive harmonic current T of mass 1. The current T can be obtained by an Ahlfors type construction starting with a arbitrary leaf of X.

math.CV↗

arXiv2000

On the commuting holomorphic endomorphisms of P^k

Let f_1, f_2 be holomorphic endomorphisms of P^k, of degrees d_1\geq 2, d_2\geq 2. Assume that f_1\circ f_2=f_2\circ f_1 and that d_1^{n_1}\not =d_2^{n_2} for all integers n_1, n_2. We then show that f_j are critically finite. Moreover there is an orbifold (P^k,n) such that f_1, f_2 are coverings of (P^k,n). In the P^2 case we give the list of commuting pairs satisfying the above conditions.

math.CV↗