Bounded hyperbolic components of bicritical rational maps

Hongming Nie; Kevin M. Pilgrim

doi:10.3934/jmd.2022016

Article Contents

2022, Volume 18: 533-553. Doi: 10.3934/jmd.2022016

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Bounded hyperbolic components of bicritical rational maps

Hongming Nie^{1, 2,} and
Kevin M. Pilgrim^3,

1.
Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram. Jerusalem, 9190401, Israel
2.
Current address: Institute for Mathematical Sciences, Stony Brook University, 100 Nicolls Road, Stony Brook, NY 11794, USA
3.
Department of Mathematics, Indiana University, 831 E 3rd St, Bloomington, IN 47405, USA

Received: April 9, 2020

Revised: May 26, 2022

Published online: November 3, 2022

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Abstract

We prove that the hyperbolic components of bicritical rational maps having two distinct attracting cycles each of period at least two are bounded in the moduli space of bicritical rational maps. Our arguments rely on arithmetic methods.

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Mathematics Subject Classification: Primary: 37F20; Secondary: 37F44, 37P50.

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References

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