Sur la construction de mesures selles

Deux caracterisations de la mesure d'equilibre d'un endomorphisme de Pk(C)

Let $μ$ be the equilibrium measure of an endomorphism of ${\sf P}^k({\bf C})$. We show that it is its unique measure of maximal entropy. We build $μ$ directly as the distribution of any point outside an algebraic exceptional set.

Bernoulli coding map and almost sure invariance principle for endomorphisms of $\mathbb{P}^k$

Let $f$ be an holomorphic endomorphism of $\mathbb{P}^k$ and $μ$ be its measure of maximal entropy. We prove an Almost Sure Invariance Principle for the systems $(\mathbb{P}^k,f,μ)$. Our class $\cal{U}$ of observables includes the Hölder functions and unbounded ones which present analytic singularities. The proof is based on a geometric construction of a Bernoulli coding map $ω: (Σ, s, ν) \to (\mathbb{P}^k,f,μ)$. We obtain the invariance principle for an observable $ψ$ on $(\mathbb{P}^k,f,μ)$ by applying Philipp-Stout's theorem for $χ= ψ\circ ω$ on $(Σ, s, ν)$. The invariance principle implies…

Equidistribution of varieties for endomorphisms of projective spaces

Let f be a non-invertible holomorphic endomorphism of the complex projective space P^k and f^n its iterate of order n. Let V be an algebraic subvariety of P^k which is generic in the Zariski sense. We give here a survey on the asymptotic equidistribution of the sequence $f^{-n}(V)$ when n goes to infinity.

紧致凯勒流形上全纯自同态下正闭流的逆像

Inverse images of positive closed currents under holomorphic endomorphisms of compact Kähler manifolds

研究紧致凯勒流形上全纯自同态下正闭流的逆像，通过证明存在恰当不变解析子集\(E\)，得出若正闭\((p,p)\)-流\(S\)在\(E\)邻域可由光滑形式表示，相关序列指数快速收敛到\(0\)的结论。

Fibrations meromorphes sur certaines varietes de classe canonique triviale

Motivated by an example, due to Voisin, of a smooth simply-connected projective variety with trivial canonical class and cyclic Picard group, admitting a meromorphic endomorphism of high degree, we study meromorphic fibrations on certain varieties with trivial canonical class. We show (theorem 2.1) that any nontrivial meromorphic fibration of a variety with trivial canonical class and cyclic Picard group is in varieties of general type. Therefore, Voisin's endomorphism cannot preserve a fibration, at least in the generic case. As this example is symplectic, we study meromorphic fibrations on s…