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1 March 2001 The residual index and the dynamics of holomorphic maps tangent to the identity
Marco Abate
Duke Math. J. 107(1): 173-207 (1 March 2001). DOI: 10.1215/S0012-7094-01-10719-9

Abstract

Let f be a (germ of ) holomorphic self-map of ℂ2 such that the origin is an isolated fixed point and such that dfO=id. Let v(f) be the degree of the first nonvanishing term in the homogeneous expansion of f−id. We generalize to ℂ2 the classical Leau-Fatou flower theorem proving that there exist v(f)−1 holomorphic curves f-invariant, with the origin in their boundary, and attracted by O under the action of f.

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Marco Abate. "The residual index and the dynamics of holomorphic maps tangent to the identity." Duke Math. J. 107 (1) 173 - 207, 1 March 2001. https://doi.org/10.1215/S0012-7094-01-10719-9

Information

Published: 1 March 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1015.37035
MathSciNet: MR1815255
Digital Object Identifier: 10.1215/S0012-7094-01-10719-9

Subjects:
Primary: 32H50
Secondary: 32S65, 37F10

Rights: Copyright © 2001 Duke University Press

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Vol.107 • No. 1 • 1 March 2001
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