Bifurcation currents in holomorphic families of rational maps
Fran\c{c}ois Berteloot
TL;DR
This paper explores bifurcations in holomorphic families of rational maps using ergodic and pluripotential theory to understand stability and dynamics.
Contribution
It introduces new methods combining ergodic and pluripotential theory to analyze bifurcations in rational maps.
Findings
Characterization of bifurcation loci
Application of pluripotential theory to dynamics
Insights into stability regions
Abstract
The aim of these lectures is the study of bifurcations within holomorphic families of polynomials or rational maps by mean of ergodic and pluripotential theoretic tools.
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Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals · Geometry and complex manifolds