The parameter space of cubic laminations with a fixed critical leaf

Academic Article

Abstract

  • © Cambridge University Press, 2016. 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.
  • Published In

    Digital Object Identifier (doi)

    Author List

  • Blokh A; Oversteegen L; Ptacek R; Timorin V
  • Start Page

  • 2453
  • End Page

  • 2486
  • Volume

  • 37
  • Issue

  • 8