The dynamics of maps tangent to the identity and with nonvanishing index

DOI10.1090/S0002-9947-08-04533-9zbMath1178.32012arXivmath/0501537MaRDI QIDQ3617626

Laura Molino

Publication date: 30 March 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501537

zbMATH Keywords

residual indexparabolic curveholomorphic map tangent to the identity

Mathematics Subject Classification ID

(q)-convexity, (q)-concavity (32F10) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Dynamical systems over complex numbers (37F99)

Related Items (10)

Fatou Flowers and Parabolic Curves ⋮ A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions ⋮ Stable Manifolds of Two-dimensional Biholomorphisms Asymptotic to Formal Curves ⋮ A note on attracting domains for holomorphic maps in ℂ2 tangent to the identity ⋮ Characteristic directions of two-dimensional biholomorphisms ⋮ Quasi-parabolic analytic transformations of \(\mathbb C^n\) ⋮ Birational properties of tangent to the identity germs without non‐degenerate singular directions ⋮ A Poincaré-Bendixson theorem for meromorphic connections on Riemann surfaces ⋮ Attracting domains for semi-attractive and quasi-attractive analytic transformations ⋮ A Fatou type theorem for complex map germs

Cites Work

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• Attracting basins for automorphisms of \(\mathbb{C}^2\)
• Invariant varieties through singularities of holomorphic vector fields
• Complex dynamics
• The residual index and the dynamics of holomorphic maps tangent to the identity
• Parabolic curves in \(\mathbb{C}^3\)
• Index theorems for holomorphic self-maps
• Analytic transformations of \((\mathbb{C}^p,0)\) tangent to the identity
• Diagonalization of nondiagonalizable discrete holomorphic dynamical systems

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