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arXiv · 1501.05568

The parameter space of cubic laminations with a fixed critical leaf

Alexander Blokh·Lex Oversteegen·Ross Ptacek·Vladlen Timorin
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Abstract

Thurston parameterized quadratic invariant laminations with a non-invariant lamination, the quotient of which yields a combinatorial model for the Mandelbrot set. As a step toward generalizing this construction to cubic polynomials, we consider slices of the family of cubic invariant laminations defined by a fixed critical leaf with non-periodic endpoints. We parameterize each slice by a lamination just as in the quadratic case, relying on the techniques of smart criticality previously developed by the authors.

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Alexander Blokh, Lex Oversteegen, Ross Ptacek, Vladlen Timorin. 2015-01-22. The parameter space of cubic laminations with a fixed critical leaf. https://arxiv.org/abs/1501.05568

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