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6 papers · 1 filter
Chaotic Period Doubling
V. V. M. S. Chandramouli, M. Martens, W. de Melo +1
The period doubling renormalization operator was introduced by M. Feigenbaum and by P. Coullet and C. Tresser in the nineteen-seventieth to study the asymptotic small scale geometr…
Teichmuller theory of the punctured solenoid
R. C. Penner, Dragomir Saric
The punctured solenoid is an initial object for the category of punctured surfaces with morphisms given by finite covers branched only over the punctures. The (decorated) Teich…
Combinatorial rigidity for unicritical polynomials
Artur Avila, Jeremy Kahn, Mikhail Lyubich +1
We prove that any unicritical polynomial which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies t…
Local connectivity of Julia sets for unicritical polynomials
Jeremy Kahn, Mikhail Lyubich
We prove that the Julia set of at most finitely renormalizable unicritical polynomial with all periodic points repelling is locally connected. (For …
Hausdorff dimension and conformal measures of Feigenbaum Julia sets
Artur Avila, Mikhail Lyubich
We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon'', there exist many Feigenbaum Julia s…
Infinitesimal contraction of the Feigenbaum renormalization operator in the horizontal direction
Daniel Smania
In this short note, we give a sketch of a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the Feigenbaum fixed point. The…