On the size of linearization domains
2008 ◽
Vol 145
(2)
◽
pp. 443-456
Keyword(s):
AbstractAssume $f{:}\,U\subset \C\to \C$ is a holomorphic map fixing 0 with derivative λ, where 0 < |λ| ≤ 1. If λ is not a root of unity, there is a formal power series φf(z) = z + ${\cal O}$(z2) such that φf(λ z) = f(φf(z)). This power series is unique and we denote by Rconv(f) ∈ [0,+∞] its radius of convergence. We denote by Rgeom(f) the largest radius r ∈ [0, Rconv(f)] such that φf(D(0,r)) ⊂ U. In this paper, we present new elementary techniques for studying the maps f ↦ Rconv(f) and f ↦ Rgeom(f). Contrary to previous approaches, our techniques do not involve studying the arithmetical properties of rotation numbers.
2002 ◽
Vol 30
(12)
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pp. 761-770
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2003 ◽
Vol 184
(2)
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pp. 369-383
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Keyword(s):
2004 ◽
Vol 339
(8)
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pp. 533-538
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2002 ◽
Vol 51
(3)
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pp. 403-410
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2017 ◽
Vol 2018
(15)
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pp. 4780-4798
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Keyword(s):
2011 ◽
Vol 31
(1)
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pp. 331-343
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CYCLICITY AND UNICELLULARITY OF THE DIFFERENTIATION OPERATOR ON BANACH SPACES OF FORMAL POWER SERIES
2005 ◽
Vol 105A
(1)
◽
pp. 1-7
Keyword(s):