Geodesic
On the Kotani-Last and Schrödinger conjectures
Avila, Artur1, 2
1 CNRS, IMJ-PRG, UMR 7586, Univ Paris Diderot, Sorbonne Paris Cité, Sorbonnes Universités, UPMC Univ Paris 06, F-75013, Paris, France
2 IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil
Journal of the American Mathematical Society, Tome 28 (2015) no. 2, pp. 579-616

Voir la notice de l'article provenant de la source American Mathematical Society

In the theory of ergodic one-dimensional Schrödinger operators, the ac spectrum has been traditionally expected to be very rigid. Two key conjectures in this direction state, on the one hand, that the ac spectrum demands almost periodicity of the potential, and, on the other hand, that the eigenfunctions are almost surely bounded in the essential support of the ac spectrum. We show how the repeated slow deformation of periodic potentials can be used to break rigidity, and disprove both conjectures.
DOI : 10.1090/S0894-0347-2014-00814-6

Avila, Artur 1, 2

1 CNRS, IMJ-PRG, UMR 7586, Univ Paris Diderot, Sorbonne Paris Cité, Sorbonnes Universités, UPMC Univ Paris 06, F-75013, Paris, France
2 IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil 
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Avila, Artur. On the Kotani-Last and Schrödinger conjectures. Journal of the American Mathematical Society, Tome 28 (2015) no. 2, pp. 579-616. doi: 10.1090/S0894-0347-2014-00814-6

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