Real laminations and the topological dynamics of complex polynomials

By Jan Kiwi. 2004

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Dynamics of McMullen maps (2012, background): “For a general polynomial with connected Julia sets and without irrationally neutral cycles, Kiwi shows in [15] that the local connectivity of the Julia set is equivalent to the non-existence of wandering continua.”
A characterization of hyperbolic rational maps (2011, methodology): “Douady’s proof of monotonicity of entropy for unimodel maps [11], Rees’ descriptions of parameter spaces [30], Kiwi’s characterization of polynomial laminations [ 23 ] (using previous work of Bielefield-Fisher-Hubbard [2 ]a nd Poirier [28]), Rees, Shishikura and Tan’s studies on matings of polynomia”
Distribution of rational maps with a preperiodic critical point (2006, methodology): “It follows from the work of Kiwi [ K1 , Theorem 3] that when P has only repelling cycles, every ζ ∈ JP has a nonempty finite set of external arguments.”