University of Toronto

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20022005

most citedFault-Tolerant Quantum Dynamical Decoupling

586 citations

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10 papers · 1 filter

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 $d = 2$ …

math.DS2005

Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary

Bassam Fayad, Maria Saprykina

Let $M$ be an $m$ -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 $μ$ .…

math.DS2004★ 3 cited

Filled Julia sets with empty interior are computable

I. Binder, M. Braverman, M. Yampolsky

We show that if a polynomial filled Julia set has empty interior, then it is computable.

math.DS2004★ 1 cited

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…