This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given.
Degenerate KAM theory for partial differential equations / D. Bambusi, M. Berti, E. Magistrelli. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 250:8(2011), pp. 3379-3397. [10.1016/j.jde.2010.11.002]
Degenerate KAM theory for partial differential equations
D. BambusiPrimo
;
2011
Abstract
This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given.
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