Destruction of Invariant Tori in Pendulum-Type Equations

Author: Huang H.

Source: Journal of Differential Equations, Volume 146, Number 1, June 1998 , pp. 67-89(23)

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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.

Language: English

Document Type: Research article

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

Publication date: 1998-06-01