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math.DSDec 6, 2023
authors
  • Pierre Berger
  • Eric Bedford
  • Fabrizio Bianchi
  • Xavier Buff
  • Sylvain Crovisier
  • Tien-Cuong Dinh
  • Romain Dujardin
  • Charles Favre
  • Tanya Firsova
  • Patrick Ingram
  • Yutaka Ishii
  • Liviana Palmisano
  • Enrique Pujals
  • Jasmin Raissy
  • Sonja Štimac
  • Gabriel Vigny
institutions
  • Institut de Mathématiques de Bordeaux
  • Institut de Mathématiques de Toulouse
  • Institut National des Sciences Appliquées de Toulouse
  • Laboratoire de Mathématiques d'Orsay
  • Université Toulouse III - Paul Sabatier
arXiv abstractPDF
paper

Hénon maps: a list of open problems

arXiv:2312.03907

Abstract

We propose a set of questions on the dynamics of Hénon maps from the real, complex, algebraic and arithmetic points of view.

34 pages, 4 figures

References in corpus (11)

  • Enveloppe galoisienne d'une application rationnelle de P1
  • Equilibrium States for Center Isometries
  • Dynamics of regular birational maps in P^k
  • No elliptic points from fixed prime ends
  • Equilibrium states of endomorphisms of Pk II: spectral stability and limit theorems
  • Every complex H{é}non map is exponentially mixing of all orders and satisfies the CLT
  • Polynomials with many rational preperiodic points
  • Analytic pseudo-rotations
  • Local rigidity of Julia sets
  • The pruning front conjecture, folding patterns and classification of Hénon maps in the presence of strange attractors
  • Relation between Hénon maps with biholomorphic escaping sets
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