Discrete holomorphic local dynamical systems

2009/03/19 by Marco Abate, Abate, Marco · 2 citations
Mathematics · Physics and Astronomy · #30D05 (Secondary) #32H50 #37F99 (Primary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.0903.3289

openalex publication_date 2009/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a vast bibliography. It updates and enlarge the previous survey arXiv:math/0310089v1.

Citations

• Linearization of holomorphic germs with resonant linear part

Cited by

• Simultaneous linearization of holomorphic germs in presence of resonances
• Poincaré-Bendixson theorems for meromorphic connections and homogeneous vector fields
• Capacity dimension of the Brjuno set in ℂⁿ

Related

• Discrete local holomorphic dynamics
• Fixed points and dynamics of holomorphic maps
• Open problems in local discrete holomorphic dynamics
• A brief survey on local holomorphic dynamics in higher dimensions
• On Closed Invariant Sets in Local Dynamics