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The parameter space of cubic laminations with a fixed critical leaf

  • ALEXANDER BLOKH (a1), LEX OVERSTEEGEN (a1), ROSS PTACEK (a2) and VLADLEN TIMORIN (a2) (a3)
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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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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