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Berkovich dynamics of Newton maps

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Abstract

Let \({\mathbb {L}}\) be the completion of the formal Puiseux series over \({\mathbb {C}}\), and let \({\textbf{P}}^1\) be the Berkovich space over \({\mathbb {L}}\). We study the dynamics of Newton maps, defined over \({\mathbb {L}}\), on \({\textbf{P}}^1\). As an application, we give a complete description of the rescaling limits for a holomorphic family of complex Newton maps.

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Acknowledgements

Partial results in this work are from the author’s thesis. He would like to thank his advisor Kevin Pilgrim for fruitful discussions. He also thanks Jan Kiwi, Laura DeMarco and Juan Rivera-Letelier for valuable comments and thanks Matthieu Arfeux and Ken Jacobs for useful conversations. The author is grateful to the referee for careful reading and invaluable suggestions.

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  1. Institute for Mathematical Sciences, Stony Brook University, 100 Nicolls Rd, Stony Brook, NY, 11794, USA

    Hongming Nie

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  1. Hongming Nie
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Nie, H. Berkovich dynamics of Newton maps. Math. Z. 304, 67 (2023). https://doi.org/10.1007/s00209-023-03324-4

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