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Necessary conditions for the existence of wandering triangles for cubic laminations
1.  Department of Mathematics, University of Alabama in Birmingham, University Station, Birmingham, AL 352941170, United States 
In this paper for a closed lamination on the unit circle invariant under $z\mapsto z^3$ (cubic lamination) we prove that if it has a wandering triangle then there must be two distinct recurrent critical points in the corresponding quotient space ("topological Julia set") $J$ with the same limit set coinciding with the limit set of any wandering vertex (wandering vertices in $J$ correspond to wandering gaps in the lamination).
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