Jiangong You
Publications:
|
Xu J., You J.
Persistence of Hyperbolic-type Degenerate Lower-dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems
2020, vol. 25, no. 6, pp. 616-650
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.
|
|
Xu J., You J.
Persistence of Hyperbolic-type Degenerate Lower-dimensional Invariant Tori with Prescribed Frequencies in Hamiltonian Systems
, , pp. 616-650
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.
|