A Cantor-Mandelbrot-Sierpiński tree in the parameter plane for rational maps

Devaney, Robert L.

doi:10.1090/s0002-9947-2013-05948-x

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…It has been shown in [5] that there exist Cantor necklaces in the parameter plane, so our results suggest that Sierpiński components and parameters whose critical orbits have kneading sequences with infinite s-part, are arranged in the parameter plane following a tree-like structure. A result in this direction can be found in [6] for the case n = 2.…”

Section: 2mentioning

confidence: 72%

A combinatorial invariant for escape time Sierpiński rational maps

Rocha

2013

Fund. Math.

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An escape time Sierpiński map is a rational map drawn from the Mc-Mullen family z → z n + λ/z n with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum. We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits. We show that each escape time Sierpiński map realizes a subgraph of the combinatorial tree and the combinatorial information is a complete conjugacy invariant.

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