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Accurate strategies for small divisor problems
Author(s):
R.
de la Llave;
David
Rana
Journal:
Bull. Amer. Math. Soc.
22
(1990),
85-90.
MSC (1985):
Primary 39-04, 39B99, 70K50, 58F27;
Secondary 65J15, 30D05, 58F30, 58F10
MathSciNet review:
1008096
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Additional information
References:
- [A] V. I. Arnold, Geometric methods in the theory of ordinary differential equations, Springer-Verlag, Berlin and New York, 1983. MR 695786
- [CC] A. Celletti and L. Chierchia, Construction of analytic K.A.M. surfaces and effective stability bounds, Comm. Math. Phys. 118 (1988), 119-161. MR 954678
- [BZ] D. Braess and E. Zehnder, On the numerical treatment of a small divisor problem, Numer. Math. 39 (1982), 269-292. MR 669322
- [L] O. E. Lanford III, Computer assisted proofs in analysis, Physica 124A (1984), 465-470. MR 759197
- [LT] C. A. Liverani, G. Servizi, and G. Turchetti, Some K.A.M. estimates for C L. Seigel's center problem, Lett. Nuovo Cimento 39 (1984), 417-423. MR 746559
- [M] R. E. Moore, Methods and applications of interval analysis, SIAM Philadelphia, 1979. MR 551212
- [Mo] J. Moser, Is the solar system stable?, Math. Intelligencer 1 (1978), 65-71. MR 495314
- [MP] R. MacKay and I. C. Percival, Converse K.A.M.: Theory and Practice, Comm. Math. Phys. 98 (1985), 469-512. MR 789867
- [R] D. Rana, Proof of accurate upper and lower bounds to stability domains in small denominator problems, Thesis, Prinecton Univ., 1987.
- [S] J. Stark, An exhaustive criterion for the non-existence of invariant circles for area-preserving twist maps, Comm. Math. Phys. 117 (1988), 177-189. MR 946999
- [Z] E. Zehnder, Generalized implicit function theorems and applications to some small divisor problems, Comm. Pure Appl. Math. 28 (1975), 91-140; 29 (1975), 49-111. MR 380867
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39-04, 39B99, 70K50, 58F27, 65J15, 30D05, 58F30, 58F10
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39-04, 39B99, 70K50, 58F27, 65J15, 30D05, 58F30, 58F10
Additional Information:
DOI:
10.1090/S0273-0979-1990-15848-3
PII:
S 0273-0979(1990)15848-3
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