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The parameter space of cubic laminations with a fixed critical leaf

Published online by Cambridge University Press:  26 July 2016

ALEXANDER BLOKH ,
LEX OVERSTEEGEN ,
ROSS PTACEK  and
VLADLEN TIMORIN
ALEXANDER BLOKH
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA email [email protected], [email protected]
LEX OVERSTEEGEN
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA email [email protected], [email protected]
ROSS PTACEK
Affiliation:
Faculty of Mathematics, National Research University Higher School of Economics, Vavilova St. 7, 112312 Moscow, Russia email [email protected]
VLADLEN TIMORIN
Affiliation:
Faculty of Mathematics, National Research University Higher School of Economics, Vavilova St. 7, 112312 Moscow, Russia email [email protected] Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia email [email protected]
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 8 , December 2017 , pp. 2453 - 2486
Copyright
© Cambridge University Press, 2016 

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