The parameter space of cubic laminations with a fixed critical leaf

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.

40 pages; 2 figures; to appear in Ergodic Theory and Dynamical Systems

References in corpus (2)

• Central Strips of Sibling Leaves in Laminations of the Unit Disk
• Combinatorial models for spaces of cubic polynomials