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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 = {Liu , BaifengZhu , Wenzhuang and Xu , Leshun}, 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.

Liu , BaifengZhu , Wenzhuang and Xu , Leshun. (2021). A KAM-Type Theorem for Generalized Hamiltonian Systems. Communications in Mathematical Research . 25 (1). 37-52. doi:
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