3 citations · 10 across the 12 of their papers we have counts for
18 papers
A Mañé-Manning formula for expanding measures for endomorphisms of
Fabrizio Bianchi, Yan Mary He
Let be an integer and a holomorphic endomorphism of of algebraic degree . We introduce a volume dimension for ergodic -invariant…
Holomorphic motions of weighted periodic points
Fabrizio Bianchi, Maxence Brévard
We study the holomorphic motions of repelling periodic points in stable families of endomorphisms of . In particular, we establish an asymptotic equidistri…
Monotonicity of dynamical degrees for H{é}non-like and polynomial-like maps
Fabrizio Bianchi, Tien-Cuong Dinh, Karim Rakhimov
We prove that, for every invertible horizontal-like map (i.e., H{é}non-like map) in any dimension, the sequence of the dynamical degrees is increasing until that of maximal value,…
Exponential mixing of all orders and CLT for automorphisms of compact K{ä}hler manifolds
Fabrizio Bianchi, Tien-Cuong Dinh
We consider the unique measure of maximal entropy of an automorphism of a compact K{ä}hler manifold with simple action on cohomology. We show that it is exponentially mixing of all…
Generalized Levi currents and singular loci for families of plurisubharmonic functions
Fabrizio Bianchi, Samuele Mongodi
We show how the formalism of Levi currents on complex manifolds, as introduced by Sibony, can be used to study the analytic structure of singular sets associated to families of plu…
Strong probabilistic stability in holomorphic families of endomorphisms of and polynomial-like maps
Fabrizio Bianchi, Karim Rakhimov
We prove that, in stable families of endomorphisms of , all invariant measures whose measure-theoretic entropy is strictly larger than at a…
Equilibrium states of endomorphisms of II: spectral stability and limit theorems
Fabrizio Bianchi, Tien-Cuong Dinh
We establish the existence of a spectral gap for the transfer operator induced on by a generic holomorphic endomorphism and a suitable conti…
On minimal kernels and Levi currents on weakly complete complex manifolds
Fabrizio Bianchi, Samuele Mongodi
A complex manifold is \emph{weakly complete} if it admits a continuous plurisubharmonic exhaustion function . The minimal kernels (the loci where a…
Equilibrium states of endomorphisms of I: existence and properties
Fabrizio Bianchi, Tien-Cuong Dinh
We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on by a holomorphic endom…
Higher bifurcations for polynomial skew-products
Matthieu Astorg, Fabrizio Bianchi
We continue our investigation of the parameter space of families of polynomial skew products. Assuming that the base polynomial has a Julia set not totally disconnected and is neit…
Degeneration of quadratic polynomial endomorphisms to a Hénon map
Fabrizio Bianchi, Yûsuke Okuyama
For an algebraic family of regular quadratic polynomial endomorphisms of parametrized by and degenerating to a Hénon map at , we study th…
Hyperbolicity and bifurcations in holomorphic families of polynomial skew products
Matthieu Astorg, Fabrizio Bianchi
We initiate a parametric study of holomorphic families of polynomial skew products, i.e., polynomial endomorphisms of of the form that exten…
Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree
Fabrizio Bianchi
Given a family of polynomial-like maps of large topological degree, we relate the presence of Misiurewicz parameters to a growth condition of the postcritical volume. This allows u…
Parabolic implosion for endomorphisms of
Fabrizio Bianchi
We give an estimate of the discontinuity of the large Julia set for a perturbation of a class of maps tangent to the identity, by means of a two-dimensional Lavaurs Theorem. We ada…
Bifurcations in the elementary Desboves family
Fabrizio Bianchi, Johan Taflin
We give an example of a family of endomorphisms of whose Julia set depends continuously on the parameter and whose bifurcation locus has non empty interio…
Holomorphic motion for Julia sets of holomorphic families of endomorphisms of CP(k)
François Berteloot, Fabrizio Bianchi
We build measurable holomorphic motions for Julia sets of holomorphic families of endomorphisms of CP(k) under various equivalent notions of stability.
A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces
Marco Abate, Fabrizio Bianchi
We prove a Poincaré-Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the c…
Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k)
François Berteloot, Fabrizio Bianchi, Christophe Dupont
We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove that it is equivalent to the stability of repelling cycles a…