Matings with laminations
Abstract
We give a topological description of the space of quadratic rational maps with superattractive two-cycles: its "non-escape locus" M2 (the analog of the Mandelbrot set M) is locally connected, it is the continuous image of M under a canonical map, and it can be described as M (minus the 1/2-limb), mated with the lamination of the basilica. The latter statement is a refined version of a conjecture of Ben Wittner, which in its original version requires local connectivity of M to even be stated. Our methods of mating with a lamination also apply to dynamical matings of certain non-locally connected Julia sets.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2011
- DOI:
- 10.48550/arXiv.1112.4780
- arXiv:
- arXiv:1112.4780
- Bibcode:
- 2011arXiv1112.4780D
- Keywords:
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- Mathematics - Dynamical Systems