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4 papers · 2 filters
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 …
Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary
Bassam Fayad, Maria Saprykina
Let be an -dimensional differentiable manifold with a nontrivial circle action ${\mathcal S}= {\lbrace S_t \rbrace}_{t \in\RR}, S_{t+1}=S_t$, preserving a smooth volume .…