Holomorphic dynamics, dynamical systems and ergodic theory, complex analysis and geometry
Stability and bifurcations for families of endomorphisms of CP(k) and other complex dynamical systems,
transfer operator and statistical properties of complex dynamical systems,
parabolic implosion,
maps tangent to the identity in C^n,
meromorphic connections on Riemann surfaces,
Levi currents on complex manifolds
My Arxiv author page is here. Preprints usually appear there before than on this page.
Most of the recent papers are also on HAL.
The arXiv and Hal versions are usually not final. Please refer to the journal webpages (or email me) for the final versions of the papers below.
Equilibrium states of holomorphic endomorphisms of CP(k): spectral gap and limit theorems (with Tien-Cuong Dinh),
pdf,
arXiv,
HAL
Geometric and Functional Analysis (GAFA), to appear
(for the original version containing both this and the part I below:
pdf,
arXiv,
HAL)
An (online) seminar about this work: Video
A 4x1h30 mini-course about the work:
Lecture 1,
Lecture 2,
Lecture 3,
Lecture 4
Strong probabilistic stability in holomorphic families of endomorphisms of Pk and polynomial-like maps (with Karim Rakhimov),
pdf,
arXiv,
HAL
International Mathematics Research Notices (IMRN), to appear
Generalized Levi currents and Singular loci for families of plurisubharmonic functions (with Samuele Mongodi),
pdf,
arXiv,
Journal of Geometric Analysis, to appear
Every Hénon map is exponentially mixing of all orders and satisfies the CLT (with Tien-Cuong Dinh), 2023,
pdf,
arXiv,
HAL
Forum of Mathematics, Sigma, Volume 12, article e4, 2024
A seminar about this work: Video
Equilibrium states of holomorphic endomorphisms of CP(k) I: existence and properties (with Tien-Cuong Dinh),
pdf,
arXiv,
HAL
Journal de Mathématiques Pures et Appliquées, Volume 172, 164-201, 2023
(see above for the part II and videos of a seminar and of a mini-course on this work)
Hyperbolicity and bifurcations in holomorphic families of polynomial skew products (with Matthieu Astorg),
pdf,
arXiv,
HAL
American Journal of Mathematics, Volume 145, Number 3, 861-898, 2023
On minimal kernels and Levi currents on weakly complete complex manifolds (with Samuele Mongodi)
pdf,
arXiv,
HAL
Proceedings of the AMS, Volume 150, Issue 9, 3927–3939, 2022
Higher bifurcations for polynomial skew products (with Matthieu Astorg)
pdf,
arXiv,
HAL
Journal of Modern Dynamics, 18, 69-99, 2022
A recorded seminar about this work: Video
Degeneration of quadratic polynomial
endomorphisms to a Hénon map (with Yusuke Okuyama),
pdf,
arXiv
Indiana University Mathematics Journal, Volume 69, 2549-2570, 2020
Misiurewicz parameters and dynamical stability of polynomial-like maps
of large topological degree,
pdf,
arXiv,
HAL
Mathematische Annalen, Volume 373, 901–928, 2019
Parabolic implosion for endomorphisms of C^2,
pdf,
arXiv,
HAL
Journal of the European Mathematical Society (JEMS), Volume 21, 3709-3737, 2019
Perturbations d'exemples de Lattès et dimension de Hausdorff du lieu de bifurcation (with François Berteloot),
pdf,
arXiv,
HAL
Journal de Mathématiques Pures et Appliquées, Volume 116, 161–173, 2018
Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of CP(k) (with François Berteloot and Christophe Dupont),
pdf, arXiv,
HAL
Annales Scientifiques de l’ENS, Volume 51, Issue 1, 215-262, 2018
Bifurcations in the elementary Desboves family (with Johan Taflin),
pdf,
arXiv,
HAL
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
Horn maps of semi-parabolic Hénon maps (with Matthieu Astorg), 2024,
pdf,
arXiv
HAL
A Mané-Manning formula for expanding measures for endomorphisms of CPk (with Yan Mary He), 2023,
pdf,
arXiv
Holomorphic motions of weighted periodic points (with Maxence Brévard), 2023,
pdf,
arXiv,
HAL
Monotonicity of dynamical degrees for horizontal-like and polynomial-like maps (with Tien-Cuong Dinh and Karim Rakhimov), 2023,
pdf,
arXiv,
HAL
Exponential mixing of all orders and CLT for automorphisms of compact Kaehler manifolds (with Tien-Cuong Dinh), 2023,
pdf,
arXiv,
HAL
Statistical properties of complex Hénon maps (with Tien-Cuong Dinh), in Hénon maps: a list of open problems (Eds. C. Favre, T. Firsova, L. Palmisano, J. Raissy, G. Vigny), 2023,
arXiv
Stability and bifurcations in projective holomorphic dynamics (with François Berteloot),
pdf
Dynamical systems, Banach Center Publications, 115, Polish Acad. Sci. Inst. Math., Warsaw, 37–71, 2018.
Quantitative aspects in complex analysis, geometry, and dynamics, Springer, CEMPI Lecture Notes Series Volume of collected lecture notes of the School and Workshop ACQUA21 In preparation
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