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CRITERION FOR RAYS LANDING TOGETHER

Abstract : Let f be a polynomial with degree ≥ 2 and the Julia set J f locally connected. We give a partition of complex plane C and show that, if z, z in J f have the same itinerary respect to the partition, then either z = z or both of them lie in the boundary of a Fatou component U , which is eventually iterated to a siegel disk. As an application, we prove the monotonicity of core entropy for the quadratic polynomial family {fc = z 2 + c : fc has no Siegel disks and J fc is locally connected }.
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https://hal.archives-ouvertes.fr/hal-01139840
Contributor : Jinsong Zeng <>
Submitted on : Tuesday, April 7, 2015 - 11:03:10 AM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Document(s) archivé(s) le : Wednesday, July 8, 2015 - 10:16:28 AM

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1503.05931v1.pdf
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  • HAL Id : hal-01139840, version 1

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Jinsong Zeng. CRITERION FOR RAYS LANDING TOGETHER. 2015. ⟨hal-01139840⟩

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