In the paper the properties of the rotation number for a random family of linear non-autonomous Hamiltonian systems are considered. In particular a complex quantity - the Floquet coefficient w - for such a family is defined and studied. The rotation number is the imaginary part of w. The w is studied to discuss the convergence properties of the Weyl M-functions, the Kotani theory, and the gap-labelling phenomenon for these problems
Rotation number for nonautonomous linear Hamiltonian systems II: the Floquet coefficient / R. FABBRI; R. JOHNSON; C. NUNEZ. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - STAMPA. - 54:(2003), pp. 652-676. [10.1007/s00033-003-1057-4]
Rotation number for nonautonomous linear Hamiltonian systems II: the Floquet coefficient
FABBRI, ROBERTA;JOHNSON, RUSSELL ALLAN;
2003
Abstract
In the paper the properties of the rotation number for a random family of linear non-autonomous Hamiltonian systems are considered. In particular a complex quantity - the Floquet coefficient w - for such a family is defined and studied. The rotation number is the imaginary part of w. The w is studied to discuss the convergence properties of the Weyl M-functions, the Kotani theory, and the gap-labelling phenomenon for these problems
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