Upper-bound for the number of robust parabolic curves for a class of maps tangent to identity

DOI10.1090/S0002-9939-2010-10503-8zbMath1215.37036arXivmath/0702576OpenAlexW2052339042MaRDI QIDQ3082329

Chiara Frosini, Francesco Degli Innocenti

Publication date: 10 March 2011

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

Full work available at URL: https://arxiv.org/abs/math/0702576

zbMATH Keywords

holomorphic mapsdynamic systemparabolic curves

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Cites Work

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• Parabolic curves for diffeomorphisms in \(\mathbb C^2\)
• Complex dynamics
• Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces
• 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
• Isolated invariant curves of a foliation
• Reduction of Singularities of the Differential Equation Ady = Bdx

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