ATTRACTING DOMAINS OF MAPS TANGENT TO THE IDENTITY WHOSE ONLY CHARACTERISTIC DIRECTION IS NON-DEGENERATE
2013 ◽
Vol 24
(10)
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pp. 1350083
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Keyword(s):
Let f be a holomorphic germ on ℂ2 that fixes the origin and is tangent to the identity. Assume that f has a non-degenerate characteristic direction [v]. Hakim gave conditions that guarantee the existence of attracting domains along [v], however, when f has only one characteristic direction, these conditions are not satisfied. We prove that when [v] is unique, the existence results still hold. In particular, there is a domain Ω whose points converge to the origin along [v] and, on Ω, f is conjugate to a translation. Furthermore, if f is a global automorphism, the corresponding domain of attraction is a Fatou–Bieberbach domain.
Keyword(s):
2014 ◽
Vol 25
(01)
◽
pp. 1450003
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Keyword(s):
2014 ◽
Vol 17
(4)
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