Fatou-Julia theory in differentiable dynamics

  • Pei-Chu Hu
  • Chung-Chun Yang
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 4)

Abstract

Recently, Fornaess and Sibony [9] studied the Fatou-Julia theory of complex dynamics on the complex projective spaces P m . Zhang and Ren ([25]) studied the problems on C m and asked when a Julia set is nonempty? In the paper [12], we introduced our joint work on Fatou-Julia theory in high dimensional spaces. In particular, we proved an existence theorem of fixed points for holomorphic self-mappings on C m . We also obtained a sufficient and necessary condition of attractive fixed points and a sufficient condition of repulsive fixed points for holomorphic self-mappings on complex manifolds, and characterized attractive and repulsive cycles of continuous self-mappings on topological spaces.

Keywords

Filtration Manifold Betti 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Pei-Chu Hu
    • 1
    • 2
  • Chung-Chun Yang
    • 1
    • 2
  1. 1.Department of MathematicsShandong UniversityJinanP.R. China
  2. 2.Department of MathematicsThe Hong Kong University of Science and TechnologyKowloon, Hong KongChina

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