Geometric methods in holomorphic dynamics
Romain Dujardin
TL;DR
This paper reviews recent research in holomorphic dynamics, focusing on geometric currents, bifurcation theory, and wandering Fatou components, highlighting key developments and open problems in the field.
Contribution
It provides a comprehensive overview of current themes in holomorphic dynamics, emphasizing geometric currents and bifurcation phenomena.
Findings
Advances in understanding laminar and woven currents
Insights into bifurcation behavior in multiple variables
Progress on the wandering Fatou components problem
Abstract
In this note we review a selection of contemporary research themes in holomorphic dynamics. The main topics that will be discussed are: geometric (laminar and woven) currents and their applications, bifurcation theory in one and several variables, and the problem of wandering Fatou components.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems