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Zbl 1134.37025
Zhang, Li; Xu, Junxiang
Persistence of invariant torus in Hamiltonian systems with two-degree of freedom.
(English)
[J] J. Math. Anal. Appl. 338, No. 2, 793-802 (2008). ISSN 0022-247X

Consider the following Hamiltonian dynamical system: $.{q}=H_p(p,q), \quad .{p}=-H_q(p,q)$ where the Hamiltonian function is $H=h(p)+f(q,p)$. The classical KAM theorem asserts that if $h$ is not degenerate i.e. det$(h_{pp})\neq 0$ then most of the invariant tori can persist when $f$ is sufficiently small. In general, the nondegeneracy condition is necessary for KAM theorems. However, the Hamiltonian systems with two degrees of freedom have some special properties and so, the present paper is devoted to a KAM theorem for a class of 2D Hamiltonian systems without any nondegeneracy condition. The main tool is the so-called KAM iteration.
[Mircea Crâşmăreanu (Iaşi)]
MSC 2000:
*37J40 Perturbations, etc.
70H08 Nearly integrable Hamiltonian systems, KAM theory

Keywords: KAM theorem; KAM iteration

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