François Berteloot - Professor of Mathematics, Institut de Mathématiques de Toulouse
My research is primarily situated at the intersection of complex analysis and dynamical systems. I am particularly interested in the study of holomorphic families of rational maps, bifurcation currents, and Lyapunov exponents, utilizing tools from pluripotential theory and non-standard analysis to understand dynamical stability.
I am currently a Professor of Mathematics at the Toulouse Institute of Mathematics and member of the international faculty for the International Mathematics Master in Algeria.
Affiliations
Research Themes
- ›Holomorphic dynamics in one and several variables
- ›Pluripotential theory and complex geometry
- ›Bifurcation currents and Lyapunov exponents
- ›Structural stability of endomorphisms of ℙᵏ
- ›Lattès maps and scaling methods
- ›Proper holomorphic mappings and boundary behavior of domains in ℂ²
Selected Strengths
The Mandelbrot set is the shadow of a Julia set
Joint work with Tien-Cuong Dinh. Working within the polynomial quadratic family, we introduce a new point of view on bifurcations which naturally allows to see the seat of bifurcations as the projection of a Julia set of a complex dynamical system in dimension three.
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