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This article is cited in 10 scientific papers (total in 10 papers)
Persistence of Hyperbolic-type Degenerate Lower-dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems
Junxiang Xua, Jiangong Youb a School of Mathematics/Southeast University,
210096 Nanjing, China
b Chern Institute of Mathematics and LPMC/Nankai University,
300071 Tianjin, China
Abstract:
It is known that under Kolmogorov’s nondegeneracy condition, the nondegenerate hyperbolic invariant torus with Diophantine frequencies will persist under small perturbations, meaning that the perturbed system still has an invariant torus with prescribed frequencies. However, the degenerate torus is sensitive to perturbations. In this paper, we prove the persistence of two classes of hyperbolic-type degenerate lower-dimensional invariant tori, one of them corrects an earlier work [34] by the second author. The proof is based on a modified KAM iteration and analysis of stability of degenerate critical points of analytic functions.
Keywords:
Hamiltonian system, KAM iteration, degenerate equilibrium, invariant tori.
Received: 10.04.2020 Accepted: 20.10.2020
Citation:
Junxiang Xu, Jiangong You, “Persistence of Hyperbolic-type Degenerate Lower-dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems”, Regul. Chaotic Dyn., 25:6 (2020), 616–650
Linking options:
https://www.mathnet.ru/eng/rcd1087 https://www.mathnet.ru/eng/rcd/v25/i6/p616
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Abstract page: | 124 | References: | 31 |
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