Invariant escaping Fatou components with two rank-one limit functions for automorphisms of
Keyword(s):
Rank One
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Abstract We construct automorphisms of ${\mathbb C}^2$ , and more precisely transcendental Hénon maps, with an invariant escaping Fatou component which has exactly two distinct limit functions, both of (generic) rank one. We also prove a general growth lemma for the norm of points in orbits belonging to invariant escaping Fatou components for automorphisms of the form $F(z,w)=(g(z,w),z)$ with $g(z,w):{\mathbb C}^2\rightarrow {\mathbb C}$ holomorphic.
2014 ◽
Vol 24
(3)
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pp. 887-915
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Keyword(s):
2002 ◽
Vol 11
(3)
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pp. 339-347
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2000 ◽
Vol 143
(1-4)
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pp. 262-289
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2018 ◽
Vol 28
(4)
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pp. 043123