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Non-recurrent parameter rays of the Mandelbrot set

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arxiv 1512.08078 v1 pith:7OIXFU3I submitted 2015-12-26 math.DS

classification math.DS
keywords non-recurrentparameteranglesanglecharacteristicraysthetaconversely
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abstract

In this paper, we prove that any parameter ray at a non-recurrent angle $\theta$ lands at a non-recurrent parameter $c$ with $\theta$ a characteristic angle of $f_c$; and conversely, every non-recurrent parameter $c$ is the landing point of one or two parameter rays at non-recurrent angles, and these angles are exactly the characteristic angles of $f_c$.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The landing of parameter rays at non-recurrent critical portraits

    math.DS 2019-08 reject novelty 6.0 of 10

    Every parameter ray at a critical portrait of a degree-d (d≥2) non-recurrent polynomial lands at that polynomial.

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