activity
20002010
most citedThe absolutely continuous spectrum of the almost Mathieu operator

60 citations · 170 across the 20 of their papers we have counts for

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Showing 2008Show all

6 papers · 1 filter

math.SP200830 cited

Bulk Universality and Clock Spacing of Zeros for Ergodic Jacobi Matrices with A.C. Spectrum

Artur Avila, Yoram Last, Barry Simon

By combining some ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for OPRL in the a.c. spectral region is implied by convergence o…

math.DS200860 cited

The absolutely continuous spectrum of the almost Mathieu operator

Artur Avila

We prove that the spectrum of the almost Mathieu operator is absolutely continuous if and only if the coupling is subcritical. This settles Problem 6 of Barry Simon's list of Schrö…

math.DS20086 cited

On the regularization of conservative maps

Artur Avila

We show that smooth maps are -dense among volume preserving maps.

math.DS20087 cited

Distortion elements in

Artur Avila

We consider the group of smooth diffeomorphisms of the circle. We show that any recurrent (in the sense that is not discrete) is in fact a distortion elemen…

math.DS20083 cited

Almost localization and almost reducibility

Artur Avila, Svetlana Jitomirskaya

We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schrödinger cocycles associated to a non-perturbatively small an…

math.DS2008

Parapuzzle of the Multibrot set and typical dynamics of unimodal maps

Artur Avila, Mikhail Lyubich, Weixiao Shen

We study the parameter space of unicritical polynomials . For complex parameters, we prove that for Lebesgue almost every , the map is either hyperboli…