Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition

By Junxiang Xu, Jiangong You. 2001

72 citations recorded by the source corpus.

In this paper we prove the persistence of lower-dimensional invariant tori of integrable equations after Hamiltonian perturbations under the first Melnikov's non-resonance condition. The proof is based on an improved KAM machinery which works for the angle variable dependent normal form. By an example, we also show the necessity of the Melnikov's first non-resonance condition for the persistence of lower dimensional tori.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/347de2d80f15d5ac0fc1f9dc8c0ec28324817a3f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

1. Xindong Xu
2. Jiansheng Geng
3. Jiangong You
4. Y. Yi
5. Massimiliano Berti
6. Michela Procesi
7. P. Bolle
8. C. Procesi

In Statistical and Nonlinear Physics

1. Jiansheng Geng
2. Xindong Xu
3. Jiangong You
4. Y. Yi
5. Massimiliano Berti
6. Michela Procesi
7. P. Bolle
8. C. Procesi

Citations in the corpus

• Quasi-periodic solutions in a nonlinear Schrödinger equation (2007, methodology): “Based on original works of Melnikov [24], Eliasson [12], Kuksin [18], and Pöschel [25], the KAM method has been extensively developed in finite dimensions concerning the persistence of lower-dimensional tori in Hamiltonian systems (see [2,3,16,23,29,31,32] and references therein).”
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation (2011, methodology): “Since the normal form part is much more simpler than Bourgain’s although it depends on the angle variables θ , as in [27] the homological equations can be decomposed into a set of linear equations of dimension at most four.”