Dynamics of one-resonant biholomorphisms

DOI10.4171/JEMS/359zbMath1351.37080arXiv0912.0428WikidataQ58623168 ScholiaQ58623168MaRDI QIDQ1932208

Filippo Bracci, Dimitri Zaitsev

Publication date: 17 January 2013

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0428

zbMATH Keywords

normal formsdiscrete dynamicsresonancesbasins of attraction

Mathematics Subject Classification ID

Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Resonance in context of PDEs (35B34) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (13)

Fatou Flowers and Parabolic Curves ⋮ A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions ⋮ Fatou components with punctured limit sets ⋮ Automorphisms of \(\mathbb C^k\) with an invariant non-recurrent attracting Fatou component biholomorphic to \(\mathbb C \times (\mathbb C^\ast)^{k-1}\) ⋮ Polynomial skew-products in dimension 2: bulging and wandering Fatou components ⋮ Factoring formal maps into reversible or involutive factors. ⋮ Wandering domains arising from Lavaurs maps with Siegel disks ⋮ Small divisors in discrete local holomorphic dynamics ⋮ Dynamics of quasi-parabolic one-resonant biholomorphisms ⋮ Random local complex dynamics ⋮ Open problems in local discrete holomorphic dynamics ⋮ Classification of invariant Fatou components for dissipative Hénon maps ⋮ Periodic cycles of attracting Fatou components of type \(\mathbb{C}\times(\mathbb{C}^*)^{d-1}\) in automorphisms of \(\mathbb{C}^d\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Parabolic curves for diffeomorphisms in \(\mathbb C^2\)
• Invariant varieties through singularities of holomorphic vector fields
• Complex dynamics
• The residual index and the dynamics of holomorphic maps tangent to the identity
• Index theorems for holomorphic self-maps
• The dynamics near quasi-parabolic fixed points of holomorphic diffeomorphisms in C 2
• Discrete holomorphic local dynamical systems

This page was built for publication: Dynamics of one-resonant biholomorphisms