Fabrizio BIANCHI

Research

Research interests

Complex dynamics: stability and bifurcations for families of endomorphisms of CP(k) and polynomial-like maps, parabolic implosion, maps tangent to the identity in C^n , meromorphic connections on Riemann surfaces.

Publications

Misiurewicz parameters and dynamical stability of polynomial-like maps of large topological degree, pdf, arXiv
To apper on Mathematische Annalen

Perturbations d'exemples de Lattès et dimension de Hausdorff du lieu de bifurcation (with François Berteloot), pdf, arXiv
To appear on the Journal de Mathématiques Pures et Appliquées

Parabolic implosion for endomorphisms of C^2, pdf, arXiv
To appear on the Journal of the European Mathematical Society (JEMS)

Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k) (with François Berteloot and Christophe Dupont), pdf, arXiv
Annales Scientifiques de l’ENS, Volume 51, Issue 1, 215-262, 2018

Bifurcations in the elementary Desboves family (with Johan Taflin), pdf, arXiv
Proceedings of the AMS, Volume 145, Issue 10, 4337-4343, 2017

A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces (with Marco Abate), pdf, arXiv
Mathematische Zeitschrift, Volume 282, Issue 1, 247–272, 2016

Preprints

Degeneration of quadratic polynomial endomorphisms to a Hénon map (with Yusuke Okuyama), pdf, arXiv

Bifurcations in families of polynomial skew products (with Matthieu Astorg), pdf, arXiv

Survey

Stability and bifurcations in projective holomorphic dynamics (with François Berteloot), pdf
To appear on the Proceeding of the Simons Semester in Banach Center Dynamical systems

Other

Motions of Julia sets and dynamical stability in several complex variables, PhD Thesis, pdf

Geodesics for meromorphic connections on Riemann surfaces and dynamics of homogeneous vector fields in several complex variables, Master Thesis, pdf