Criterion for rays landing together
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Abstract:
We give a criterion to determine when two external rays land at the same point for polynomials with locally connected Julia sets. As an application, we provide an elementary proof of the monotonicity of the core entropy along arbitrary veins of the Mandelbrot set.References
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Additional Information
- Jinsong Zeng
- Affiliation: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, People’s Republic of China
- MR Author ID: 1050094
- Email: jinsongzeng@163.com
- Received by editor(s): January 17, 2018
- Received by editor(s) in revised form: August 24, 2019, November 28, 2019, January 5, 2020, and January 12, 2020
- Published electronically: May 26, 2020
- Additional Notes: The author was partially supported by the China Scholarship Council and the NSFC under grant No.11801106 during the preparation of this paper.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 6479-6502
- MSC (2010): Primary 37F45; Secondary 37F10
- DOI: https://doi.org/10.1090/tran/8088
- MathSciNet review: 4155183