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math.DSSep 26, 2021
authors
  • Romain Dujardin
institutions
  • Laboratoire de Probabilités et Modèles Aléatoires
  • Laboratoire de Probabilités, Statistique et Modélisation
arXiv abstractPDF
paper

Geometric methods in holomorphic dynamics

arXiv:2109.04185

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.

arXiv commentTo appear in the proceedings of the ICM 2022

References in corpus (10)

  • Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
  • Some aspects of explicit birational geometry inspired by complex dynamics
  • Non density of stability for holomorphic mappings on P^k
  • Stability and bifurcations for dissipative polynomial automorphisms of C^2
  • The Geometric Dynamical Northcott and Bogomolov Properties
  • Saddle hyperbolicity implies hyperbolicity for polynomial automorphisms of C^2
  • Unique Ergodicity for foliations on compact Kähler surfaces
  • Structural Instability of Semi-Siegel Hénon maps
  • Green currents for holmorphic automorphisms of compact Kahler manifolds
  • Stable intersections of regular conformal Cantor sets with large Hausdorff dimensions
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