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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2020, том 25, выпуск 6, страницы 616–650 (Mi rcd1087)

Эта публикация цитируется в 10 статьях

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

Аннотация: 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.

Ключевые слова: Hamiltonian system, KAM iteration, degenerate equilibrium, invariant tori.

MSC: 37J40, 37J25, 37J05

Поступила в редакцию: 10.04.2020
Принята в печать: 20.10.2020

Язык публикации: английский

DOI: 10.1134/S1560354720060088



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