Reduction of singularities of holomorphic maps of $\cv^2$ tangent to the identity

2013 ◽  
Vol 83 (4) ◽  
pp. 537-546 ◽  
Author(s):  
FENG RONG
Keyword(s):  
Holomorphic Maps ◽  
Reduction Of Singularities ◽  
Tangent To The Identity

THE NON-DICRITICAL ORDER AND ATTRACTING DOMAINS OF HOLOMORPHIC MAPS TANGENT TO THE IDENTITY

2014 ◽  
Vol 25 (01) ◽  
pp. 1450003 ◽  
Author(s):  
FENG RONG
Keyword(s):  
Fixed Point ◽  
Duke Math ◽  
Holomorphic Maps ◽  
Characteristic Direction ◽  
Local Dynamics ◽  
Analytic Transformation ◽  
Tangent To The Identity

We study the local dynamics of holomorphic maps f in Cn tangent to the identity at a fixed point p with a non-degenerate characteristic direction [v]. In [M. Hakim, Analytic transformation of (Cp, 0) tangent to the identity, Duke Math. J.92 (1998) 403–428], n - 1 invariants αj, 1 ≤ j ≤ n - 1, called the directors, were associated to [v] and it was shown that if Re αj > 0 for all j then f has an attracting domain at p tangent to [v]. In this paper, we study the case Re αj = 0 for some j. With the help of a new invariant μ called the non-dicritical order, we show that f has an attracting domain at p tangent to [v] if μ ≥ 1. We also study the "spiral domains" when μ = 0. For n = 2, we show that f has an attracting domain at p tangent to [v] if and only if either the director α > 0 or μ ≥ 1.

scholarly journals Interpolation by holomorphic maps from the disc to the tetrablock

2021 ◽  
Vol 498 (2) ◽  
pp. 124951
Author(s):  
Hadi O. Alshammari ◽  
Zinaida A. Lykova
Keyword(s):  
Holomorphic Maps

Spaces of Holomorphic Maps with Bounded Multiplicity

2001 ◽  
Vol 52 (2) ◽  
pp. 249-259 ◽  
Author(s):  
K. Yamaguchi
Keyword(s):  
Holomorphic Maps
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