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Perturbations of embedded eigenvalues for the bilaplacian on a cylinder
Discrete and continuous spectra on laminations over Aubry-Mather sets
1. | LAGA, CNRS UMR 7539, Université Paris 13, Villetaneuse 93430 |
The answer will essentially depend on the number of orbits of gaps in the Aubry-Mather set. More precisely, if the Aubry-Mather set has exactly one orbit of gaps and is hyperbolic then the special flow over it with any smooth ceiling function will be conjugate to a suspension with a constant ceiling function, failing hence to be weak mixing or even topologically weak mixing. To the contrary, if the Aubry-Mather set has more than one orbit of gaps with at least two in a general position then the special flow over it will in general be weak mixing.
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