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- W4302434902 abstract "We study invariant Fatou components for holomorphic endomorphisms in $mathbb{P}^2$. In the recurrent case these components were classified by Sibony and the second author in 1995. In 2008 Ueda completed this classification by proving that it is not possible for the limit set to be a punctured disk. Recently Lyubich and the third author classified non-recurrent invariant Fatou components, under the additional hypothesis that the limit set is unique. Again all possibilities in this classification were known to occur, except for the punctured disk. Here we show that the punctured disk can indeed occur as the limit set of a non-recurrent Fatou component. We provide many additional examples of holomorphic and polynomial endomorphisms of $mathbb{C}^2$ with non-recurrent Fatou components on which the orbits converge to the regular part of arbitrary analytic sets." @default.
- W4302434902 created "2022-10-06" @default.
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- W4302434902 date "2013-08-15" @default.
- W4302434902 modified "2023-09-26" @default.
- W4302434902 title "Fatou Components with Punctured Limit Sets" @default.
- W4302434902 doi "https://doi.org/10.48550/arxiv.1308.3407" @default.
- W4302434902 hasPublicationYear "2013" @default.
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