Forum Mathematicum · 2009 · 18 citations · 15 references
Natural SciencesMathematicsGeometryTopologyAlgebraic GeometryArithmetic GeometryHyperbolic GeometryCantor SetHyperbolic SetsInvariant SetsJulia SetsRational Curves
In this paper, we prove that a rational map with a Cantor Julia set carries no invariant line field on its Julia set. It follows that a structurally stable rational map with a Cantor Julia set is hyperbolic.
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Dynamics of quadratic polynomials, I–II
Mikhail Lyubich · Acta Mathematica · 1997 · 279 citations · Full text
Generic Hyperbolicity in the Logistic Family
Jacek Graczyk, Grzegorz Świa̧tek · Annals of Mathematics · 1997 · 215 citations