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- W2952349202 abstract "The Leau-Fatou flower theorem completely describes the dynamic behavior of $1-$dimensional maps tangent to the identity. In dimension two Hakim and Abate proved that if $f$ is a holomorphic map tangent to the identity in $mathbb{C}^2$ and $nu(f)$ is the degree of the first non vanishing jet of $f-Id$ then there exist $nu(f)-1$ robust parabolic curves (RP curves for short), namely attractive petals at the origin which survive under by blow-up. The set of the exponential of holomorphic vector fields (of order greater than or equal to two), $Phi_{geq 2}(mathbb{C}^2,0)$, is dense in the space of germs of maps tangent to the identity. In this paper we give an upper-bound for the number of robust parabolic curves of $fin Phi_{geq 2}(mathbb{C}^2,0) .$" @default.
- W2952349202 created "2019-06-27" @default.
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- W2952349202 date "2007-02-20" @default.
- W2952349202 modified "2023-09-27" @default.
- W2952349202 title "Upper-bound for the number of robust parabolic curves for a class of maps tangent to identity" @default.
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