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Destruction of Invariant Tori in Pendulum-Type Equations

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Abstract:

In this paper we prove that if there exists an invariant torus with the rotation number (1, omega) in the pendulum-type equation ¨x=Q0 x(t, x) for a given potential Q0=Q0(t, x)C[infinity](T2), and omega is a Liouville number, then for any neighborhood N(Q0) of Q0 in the C[infinity]topology, there exists a potential Q=Q(t, x)N(Q0) such that the system ¨x=Qx(t, x) does not admit any invariant torus with the rotation number (1, omega). This confirms J. Moser's suggestion in Bol. Soc. Brasil. Mat. 20 (1981), 29-45. Copyright 1998 Academic Press.

Document Type: Research Article

Affiliations: Institute of Mathematics, Academia Sinica, Beijing, 100080, People's Republic of China

Publication date: June 1, 1998

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