Mikhail Lyubich

most citedCombinatorial rigidity for unicritical polynomials

4 citations · 7 across the 3 of their papers we have counts for

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math.DS2005

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 $F$ in $R^{2}$ are studied. It is shown that the appropriately defined renormalizations $R^{n} F$ …

math.DS2005★ 4 cited

Combinatorial rigidity for unicritical polynomials

Artur Avila, Jeremy Kahn, Mikhail Lyubich +1

We prove that any unicritical polynomial $f_{c} : z \mapsto z^{d} + c$ which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies t…

math.DS2005★ 3 cited

Local connectivity of Julia sets for unicritical polynomials

Jeremy Kahn, Mikhail Lyubich

We prove that the Julia set $J (f)$ of at most finitely renormalizable unicritical polynomial $f : z \mapsto z^{d} + c$ with all periodic points repelling is locally connected. (For $d = 2$ …