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arXiv · 1606.04494

Reducibility of 1-d Schroedinger equation with time quasiperiodic unbounded perturbations, I

Dario Bambusi
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Abstract

We study the Schrödinger equation on $\R$ with a polynomial potential behaving as $x^{2l}$ at infinity, $1\leq l\in\N$ and with a small time quasiperiodic perturbation. We prove that if the symbol of the perturbation grows at most like $(ξ^2+x^{2l})^{β/(2l)}$, with $β<l+1$, then the system is reducible. Some extensions including cases with $β=2l$ are also proved. The result implies boundedness of Sobolev norms. The proof is based on pseudodifferential calculus and KAM theory.

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Dario Bambusi. 2016-06-14. Reducibility of 1-d Schroedinger equation with time quasiperiodic unbounded perturbations, I. https://doi.org/10.1007/s00220-016-2825-2

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