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Volume 27, Issue 1
KAM Type-Theorem for Lower Dimensional Tori in Random Hamiltonian Systems

Yong Li & Lu Xu

Commun. Math. Res., 27 (2011), pp. 81-96.

Published online: 2021-05

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  • Abstract

In this paper, we study the persistence of lower dimensional tori for random Hamiltonian systems, which shows that majority of the unperturbed tori persist as Cantor fragments of lower dimensional ones under small perturbation. Using this result, we can describe the stability of the non-autonomous dynamic systems.

  • Keywords

random Hamiltonian system, KAM type theorem, Cantor fragment of invariant tori.

  • AMS Subject Headings

37J40, 37H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-81, author = {Li , Yong and Xu , Lu}, title = {KAM Type-Theorem for Lower Dimensional Tori in Random Hamiltonian Systems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {1}, pages = {81--96}, abstract = {

In this paper, we study the persistence of lower dimensional tori for random Hamiltonian systems, which shows that majority of the unperturbed tori persist as Cantor fragments of lower dimensional ones under small perturbation. Using this result, we can describe the stability of the non-autonomous dynamic systems.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19109.html} }
TY - JOUR T1 - KAM Type-Theorem for Lower Dimensional Tori in Random Hamiltonian Systems AU - Li , Yong AU - Xu , Lu JO - Communications in Mathematical Research VL - 1 SP - 81 EP - 96 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19109.html KW - random Hamiltonian system, KAM type theorem, Cantor fragment of invariant tori. AB -

In this paper, we study the persistence of lower dimensional tori for random Hamiltonian systems, which shows that majority of the unperturbed tori persist as Cantor fragments of lower dimensional ones under small perturbation. Using this result, we can describe the stability of the non-autonomous dynamic systems.

Li , Yong and Xu , Lu. (2021). KAM Type-Theorem for Lower Dimensional Tori in Random Hamiltonian Systems. Communications in Mathematical Research . 27 (1). 81-96. doi:
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