A KAM-type Theorem for Generalized Hamiltonian Systems |
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Authors: | Liu Bai-feng Zhu Wen-zhuang Xu Le-shun |
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Affiliation: | 1. Department of Mathematics and Information Science;Shandong Institute of Business and Technology;Yantai;Shandong;264005;2. College of Mathematics;Nankai University;Tianjin;300071;3. Department of Applied Mathematics;Northwest A & F University;Yangling;Shanxi;712100 |
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Abstract: | In this paper we mainly concern the persistence of lower-dimensional invariant tori in generalized Hamiltonian systems. Here the generalized Hamiltonian systems refer to the systems which may admit a distinct number of action and angle variables. In particular, system under consideration can be odd dimensional. Under the Riissmann type non-degenerate condition, we proved that the majority of the lower-dimension invariant tori of the integrable systems in generalized Hamiltonian system are persistent under small perturbation. The surviving lower-dimensionai tori might be elliptic, hyperbolic, or of mixed type. |
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Keywords: | KAM theory invariant tori generalized Hamiltonian system |
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