Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3151-3161 |
| Number of pages | 11 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 73 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2010 Nov 15 |
| Externally published | Yes |
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Keywords
- KAM theory
- Nearly integrable Hamiltonian systems
- Quasi-periodic motions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
A point-wise criterion for quasi-periodic motions in the KAM theory. / Soga, Kohei.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 73, No. 10, 15.11.2010, p. 3151-3161.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A point-wise criterion for quasi-periodic motions in the KAM theory
AU - Soga, Kohei
PY - 2010/11/15
Y1 - 2010/11/15
N2 - 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.
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.
KW - KAM theory
KW - Nearly integrable Hamiltonian systems
KW - Quasi-periodic motions
UR - http://www.scopus.com/inward/record.url?scp=77956179555&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956179555&partnerID=8YFLogxK
U2 - 10.1016/j.na.2010.06.058
DO - 10.1016/j.na.2010.06.058
M3 - Article
AN - SCOPUS:77956179555
VL - 73
SP - 3151
EP - 3161
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 10
ER -