Abstract
We consider holomorphic maps of surfaces of complex dimension two. Such a map is said to be conservative if it preserves volume. We discuss the properties of these maps and present a number of open problems.
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Notes
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A component \(\varOmega \) is said to be wandering if \(f^n(\varOmega )\cap \varOmega =\emptyset \) for all nonzero \(n\in {\mathbb Z}\). It is an open question, in the dissipative case \(|\delta |<1\), whether polynomial automorphisms can have wandering Fatou components.
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Acknowledgements
I wish to thank Prof. Shigehiro Ushiki for generously explaining his computer work and sharing his ideas with me. His work and vision have been an inspiration and motivation for my work.
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Bedford, E. (2018). Fatou Components for Conservative Holomorphic Surface Automorphisms. In: Byun, J., Cho, H., Kim, S., Lee, KH., Park, JD. (eds) Geometric Complex Analysis. Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-13-1672-2_4
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