4 citations · 13 across the 6 of their papers we have counts for
6 papers
Renormalization in the Henon family, I: universality but non-rigidity
A. de Carvalho, M. Lyubich, M. Martens
In this paper geometric properties of infinitely renormalizable real Hénon-like maps in are studied. It is shown that the appropriately defined renormalizations …
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…
Examples of Feigenbaum Julia sets with small Hausdorff dimension
Artur Avila, Mikhail Lyubich
We give examples of infinitely renormalizable quadratic polynomials $F_c: z\maps to z^2+c$ with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close…
Note on the geometry of generalized parabolic towers
Mikhail Lyubich
The goal of this technical note is to show that the geometry of generalized parabolic towers cannot be essentially bounded. It fills a gap in author's paper "Combinatorics, geomert…