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Volume 25, Issue 1
A KAM-Type Theorem for Generalized Hamiltonian Systems

Baifeng Liu, Wenzhuang Zhu & Leshun Xu

Commun. Math. Res., 25 (2009), pp. 37-52.

Published online: 2021-05

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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 Rüssmann 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-dimensional tori might be elliptic, hyperbolic, or of mixed type.

  • Keywords

KAM theory, invariant tori, generalized Hamiltonian system.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-37, author = {Baifeng and Liu and and 18104 and and Baifeng Liu and Wenzhuang and Zhu and and 18105 and and Wenzhuang Zhu and Leshun and Xu and and 18106 and and Leshun Xu}, title = {A KAM-Type Theorem for Generalized Hamiltonian Systems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {1}, pages = {37--52}, 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 Rüssmann 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-dimensional tori might be elliptic, hyperbolic, or of mixed type.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19181.html} }
TY - JOUR T1 - A KAM-Type Theorem for Generalized Hamiltonian Systems AU - Liu , Baifeng AU - Zhu , Wenzhuang AU - Xu , Leshun JO - Communications in Mathematical Research VL - 1 SP - 37 EP - 52 PY - 2021 DA - 2021/05 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19181.html KW - KAM theory, invariant tori, generalized Hamiltonian system. AB -

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 Rüssmann 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-dimensional tori might be elliptic, hyperbolic, or of mixed type.

Baifeng Liu, WenzhuangZhu & LeshunXu. (2021). A KAM-Type Theorem for Generalized Hamiltonian Systems. Communications in Mathematical Research . 25 (1). 37-52. doi:
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