Fatou and Julia sets for entire mappings in \(\mathbb{C}^k\)

DOI10.1007/s002080050174zbMath0931.37016OpenAlexW2028679134WikidataQ122480439 ScholiaQ122480439MaRDI QIDQ1392391

Nessim Sibony, John-Erik Fornaess

Publication date: 7 March 2000

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002080050174

zbMATH Keywords

holomorphic mapsJulia setFatou setbiholomorphic mappingsnormal familyiteration of holomorphic mapsrecurrent domainsrepelling fixed pointFatou-Julia theoryempty Julia setoscillating Fatou componentswandering Fatou components

Mathematics Subject Classification ID

Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50)

Related Items (14)

A two-dimensional polynomial mapping with a wandering Fatou component ⋮ Fatou-Julia dichotomy of matrix-valued polynomials ⋮ Polynomial skew-products in dimension 2: bulging and wandering Fatou components ⋮ Dynamics of transcendental Hénon maps. II ⋮ Stochastic adding machine and 2-dimensional Julia sets ⋮ A transcendental Hénon map with an oscillating wandering short \(\mathbb{C}^2\) ⋮ Dynamics of transcendental Hénon maps ⋮ Dynamics of semigroups of entire maps of \(\mathbb C^k\) ⋮ A polynomial automorphism with a wandering Fatou component ⋮ Stochastic adding machines based on Bratteli diagrams ⋮ Automorphisms of \(\mathbb{C}^m\) with bounded wandering domains ⋮ Nonexistence of wandering domains for strongly dissipative infinitely renormalizable Hénon maps at the boundary of chaos ⋮ Emergence of wandering stable components ⋮ Dynamics of generic endomorphisms of Oka-Stein manifolds

This page was built for publication: Fatou and Julia sets for entire mappings in \(\mathbb{C}^k\)