Quadratic Julia Sets with Positive Area

Mathematics – Dynamical Systems

Scientific paper

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57 pages. In this update, we added lots of figures and detailed the proofs, especially in the section called "the control of t

Scientific paper

We prove the existence of quadratic polynomials having a Julia set with
positive Lebesgue measure in three cases: the presence of a Cremer fixed point,
the presence of a Siegel disk, the presence of infinitely many (satellite)
renormalizations.

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