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On the core entropy of Newton maps

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Abstract

In this paper, we define the core entropy for postcritically-finite Newton maps and study its continuity within this family. We show that the entropy function is not continuous in this family, which is different from the polynomial case, and describe completely the continuity of the entropy function at the generic parameters.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11871354 and 12131016). The author thanks Laura DeMarco for very helpful discussion and suggestions. The author is also grateful for the referees’ comments and suggestions for this paper.

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  1. Department of Mathematics, Shenzhen University, Shenzhen, 518060, China

    Yan Gao

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  1. Yan Gao
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Correspondence to Yan Gao.

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Gao, Y. On the core entropy of Newton maps. Sci. China Math. 67, 77–128 (2024). https://doi.org/10.1007/s11425-021-2010-1

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