Laminations in the language of leaves (Q2847199)

The authors state the definitions of invariant laminations, a clean lamination, given by Thurston, and \(q\)-laminations which form an important class of laminations many of which correspond to complex polynomials with connected Julia sets.NEWLINENEWLINEIn this article the authors introduce a new notion of sibling invariant lamination which is slightly more restrictive that the one given by Thurston. The authors show that the family of all sibling invariant laminations is closed and contains all \(q\)-laminations. They also show that clean laminations are \(q\)-laminations, then they apply these ideas to the degree two case and show that in this case all clean Thurston invariant laminations are \(q\)-laminations.