We study the Schrodinger equation on R with a polynomial potential behaving as x(21) at infinity, 1 <= l is an element of N, and with a small time quasiperiodic perturbation. We prove that if the symbol of the perturbation grows at most like (xi(2) + x(2l))(beta/(2l)), with beta < l + 1, then the system is reducible. Some extensions including cases with beta = 2l are also proved.
Reducibility of 1-D Schroedinger equation with time quasiperiodic unbounded perturbations. I / D. Bambusi. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 370:3(2018), pp. 1823-1865. [10.1090/tran/7135]
Reducibility of 1-D Schroedinger equation with time quasiperiodic unbounded perturbations. I
D. Bambusi
2018
Abstract
We study the Schrodinger equation on R with a polynomial potential behaving as x(21) at infinity, 1 <= l is an element of N, and with a small time quasiperiodic perturbation. We prove that if the symbol of the perturbation grows at most like (xi(2) + x(2l))(beta/(2l)), with beta < l + 1, then the system is reducible. Some extensions including cases with beta = 2l are also proved.
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