Kolmogorov condition for integrable systems with focus-focus singularities

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 215, Issue 1-2, 1996, Pages 40-44

  Zung, Nguyen Tien ^a  

^a UNIV MONTPELLIER   (France)

Author keywords

Integrable system; KAM theory; Singularity

Indexed keywords

COMPUTATIONAL COMPLEXITY; DEGREES OF FREEDOM (MECHANICS);

INTEGRABLE HAMILTONIAN SYSTEM; INTEGRABLE SYSTEMS; KAM THEOREM; KAM THEORY; KOLMOGOROV; NON-DEGENERACY; SINGULARITY; TWO DEGREES OF FREEDOM;

HAMILTONIANS;

EID: 0041581444     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/0375-9601(96)00219-8     Document Type: Article

References (14)

1. L. Bates, Z. Angew. Math. Phys. 42 (1991) 837.
2. R. Cushman and H. Knörrer, Lecture notes in mathematics, Vol. 1139. The energy momentum mapping of the Lagrange top (Spriner, Berlin, 1985) p. 12.
3. J.J. Duistermaat, Comm. Pure Appl. Math. 33 (1980) 687.
4. L.H. Eliasson, Comm. Math. Helv. 65 (1990) 4.
5. E. Horozov, J. Reine Angew. Math. 408 (1990) 114.
6. H. Knörrer, J. Reine Angew. Math. 355 (1985) 67.
7. L. Lerman and Ya. Umanskii, Selecta Math. Sov. 6 (1987) 365; 7 (1988) 39.
8. L. Lerman and Ya. Umanskii, Selecta Math. Sov. 6 (1987) 365; 7 (1988) 39.
9. J. Moser, Stable and random motions in dynamical systems, Ann. Math. Studies 77 (Princeton, 1973).
10. A.A. Oshemkov, Adv. Sov. Math. 6 (1991) 67.
11. S. Wojciechowski, Hamiltonian structures and complete integrability in analytical mechanics, in: Soliton theory: a survey of results, ed. A. Fordy (1990) pp. 235-272.
12. M. Zou, Phys. Lett. A 166 (1992) 321.
13. Nguyen Tien Zung, A note on focus-focus singularities, Diff. Geom. Appl., to appear.
14. Nguyen Tien Zung, Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities, Compositio Math., to appear.