A point-wise criterion for quasi-periodic motions in the KAM theory

研究成果: Article

1 引用 (Scopus)

抄録

We consider initial value problems for nearly integrable Hamiltonian systems. We formulate a sufficient condition for each initial value to admit the quasi-periodic solution with a Diophantine frequency vector, without any nondegeneracy of the integrable part. We reconstruct the KAM theorem under Rssmann's nondegeneracy by the measure estimate for the set of initial values satisfying this sufficient condition. Our point-wise version is of the form analogous to the corresponding problems for the integrable case. We compare our framework with the standard KAM theorem through a brief review of the KAM theory.

元の言語English
ページ(範囲)3151-3161
ページ数11
ジャーナルNonlinear Analysis, Theory, Methods and Applications
73
発行部数10
DOI
出版物ステータスPublished - 2010 11 15
外部発表Yes

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KAM Theorem
Quasi-periodic Motion
KAM Theory
Hamiltonians
Initial value problems
Nondegeneracy
Quasi-periodic Solutions
Integrable Hamiltonian System
Sufficient Conditions
Initial Value Problem
Estimate
Form
Framework
Review
Standards

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

これを引用

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AB - We consider initial value problems for nearly integrable Hamiltonian systems. We formulate a sufficient condition for each initial value to admit the quasi-periodic solution with a Diophantine frequency vector, without any nondegeneracy of the integrable part. We reconstruct the KAM theorem under Rssmann's nondegeneracy by the measure estimate for the set of initial values satisfying this sufficient condition. Our point-wise version is of the form analogous to the corresponding problems for the integrable case. We compare our framework with the standard KAM theorem through a brief review of the KAM theory.

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KW - Nearly integrable Hamiltonian systems

KW - Quasi-periodic motions

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