Abstract
We generalize the classification of recurrent domains for holomorphic maps on two-dimensional complex projective space given in Fornæss and Sibony (Math. Ann. 301:813–820, 1995) to higher dimensions. In particular, we show that an invariant recurrent Fatou component is either an attracting basin or a Siegel domain or it retracts to a lower-dimensional Siegel manifold.
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Acknowledgements
We would like to thank the referee for the critical comments which clarified part of the proof of the main theorem. Part of the work was done while the second named author was visiting the Department of Mathematics at University of Michigan, the Mathematical Sciences Center at Tsinghua University, and the Institute for Mathematics at Norwegian University of Science and Technology. He would like to thank the hosts for their hospitality and support.
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Communicated by Steven R. Bell.
The first author is partially supported by grant DMS-1006294 from the National Science Foundation.
The second author is partially supported by grant 11001172 from the National Natural Science Foundation of China, grant 20100073120067 from the Specialized Research Fund for the Doctoral Program of Higher Education of China, and a grant from the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars.
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Fornæss, J.E., Rong, F. Classification of Recurrent Domains for Holomorphic Maps on Complex Projective Spaces. J Geom Anal 24, 779–785 (2014). https://doi.org/10.1007/s12220-012-9355-8
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DOI: https://doi.org/10.1007/s12220-012-9355-8