arXiv subjects
Publications and source records attributed to Henry de Thelin.
We prove general mixing theorems for sequences of meromorphic maps on compact Kähler manifolds. We deduce that the bifurcation measure is exponentially mixing for a family of rational maps of $\mathbb{P}^q(\mathbb{C})$ endowed with suitably many marked points.
Let $X$ be a compact complex manifold of dimension $k$ and $f:X \longrightarrow X$ be a dominating meromorphic map. We generalize the notion of topological entropy, by defining a quantity $h_{(m,l)}^{top}(f)$ which measures the action of $f$ on local analytic sets $W$ of dimension $l$ with $W \subset f^{-n}(Δ)$ where $Δ$ is a local analytic set of dimension $m$. We give then inequalities between $h_{(m,l)}^{top}(f)$ and Lyapounov exponents of suitable invariant measures.
We give a lower bound for the Hausdorff dimension of the support of the Green current associated to some meromorphic maps.
We construct a space which is useful in order to study the entropy of meromorphic maps by using projective limits. We deduce a variational principle for meromorphic maps.
Let $f:X\to X$ be a dominating meromorphic map of a compact Kähler surface of large topological degree. Let $S$ be a positive closed current on $X$ of bidegree $(1,1)$. We consider an ergodic measure $ν$ of large entropy supported by $\mathrm{supp}(S)$. Defining dimensions for $ν$ and $S$, we give inequalities à la Mañé involving the Lyapunov exponents of $ν$ and those dimensions. We give dynamical applications of those inequalities.
We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.
We study random holomorphic endomorphisms of P^k(C). This article is the second part of arXiv:1205.1601
We study random holomorphic endomorphisms of P^k(C). Under some assumptions, we construct a random Green current and a random Green measure and we prove that these measures have mixing properties.
Let f be a dominating meromorphic self-map of a compact Kahler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of f using the metric entropy and the dynamical degrees of f. We deduce the hyperbolicity of some measures.
We give a construction of measures with partial sum of Lyapunov exponents bounded by below.
We show that a sequence of smooth analytic subsets of dimension s of the unit ball of C^l, for which the curvature is bounded by the volume, converges to a lamination of dimension s in a weak sense.
We show that the main part of the genus of the preimages of a projective line by a generic holomorphic endomorphism of CP^2 goes to the support of the Green measure.
We give a short proof of Ahlfors' theorem on covering surfaces.
We build saddle measures (in a weak sense) for holomorphic endomorphisms of CP^2.