A Fatou type theorem for complex map germs

DOI10.1090/S1088-4173-2012-00242-1zbMath1271.32034OpenAlexW1979542800MaRDI QIDQ2842884

Bruno C. Azevedo Scárdua, Leonardo Meireles Câmara

Publication date: 19 August 2013

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1088-4173-2012-00242-1

zbMATH Keywords

parabolic curvecomplex diffeomorphism germformal separatrix

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Singularities of holomorphic vector fields and foliations (32S65) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Dynamical systems over complex numbers (37F99) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (3)

Fatou Flowers and Parabolic Curves ⋮ Parabolic curves of diffeomorphisms asymptotic to formal invariant curves ⋮ NOWHERE‐ANALYTIC SMOOTH CURVES WITH NON‐TRIVIAL ANALYTIC ISOTROPY

Cites Work

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• On the integrability of holomorphic vector fields
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• Invariant varieties through singularities of holomorphic vector fields
• Complex dynamics
• Groups of germs of analytic diffeomorphisms in \(({\mathbb C}^2,0)\)
• The residual index and the dynamics of holomorphic maps tangent to the identity
• Analytic transformations of \((\mathbb{C}^p,0)\) tangent to the identity
• The dynamics of maps tangent to the identity and with nonvanishing index
• Reduction of Singularities of the Differential Equation Ady = Bdx
• Algèbre

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