Zobrazeno 1 - 10
of 309
pro vyhledávání: '"Avila, Artur"'
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by H\"older continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded distortion pr
Externí odkaz:
http://arxiv.org/abs/2402.00215
Autor:
Avila, Artur
We show that a one-frequency analytic SL(2,R) cocycle with Diophantine rotation vector is analytically linearizable if and only if the Lyapunov exponent is zero through a complex neighborhood of the circle. More generally, we show (without any arithm
Externí odkaz:
http://arxiv.org/abs/2307.11071
We solve the Dry Ten Martini Problem in the non-critical case, i.e., all possible spectral gaps are open for almost Mathieu operators with $\lambda\ne \pm 1$.
Externí odkaz:
http://arxiv.org/abs/2306.16254
We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any compactly
Externí odkaz:
http://arxiv.org/abs/2305.06009
We consider Schr\"odinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a connected compact
Externí odkaz:
http://arxiv.org/abs/2211.02173
We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators. For the class of critical coupli
Externí odkaz:
http://arxiv.org/abs/2110.07974
We establish a dichotomy for the rate of the decay of the Ces\`aro averages of correlations of sufficiently regular functions for typical interval exchange transformations (IET) which are not rigid rotations (for which weak mixing had been previously
Externí odkaz:
http://arxiv.org/abs/2105.10547
We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant H\"older continuous
Externí odkaz:
http://arxiv.org/abs/2011.10146
In this paper we study spectral properties of Schr\"odinger operators with quasi-periodic potentials related to quasi-periodic action minimizing trajectories for analytic twist maps. We prove that the spectrum contains a component of absolutely conti
Externí odkaz:
http://arxiv.org/abs/2004.09137