Accurate strategies for small divisor problems
Authors:
R. de la Llave and David Rana
Journal:
Bull. Amer. Math. Soc. 22 (1990), 8590
MSC (1985):
Primary 3904, 39B99, 70K50, 58F27; Secondary 65J15, 30D05, 58F30, 58F10
DOI:
https://doi.org/10.1090/S027309791990158483
MathSciNet review:
1008096
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[A] V. I. Arnold, Geometric methods in the theory of ordinary differential equations, SpringerVerlag, 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), 119161. MR 954678

[BZ] D. Braess and E. Zehnder, On the numerical treatment of a small divisor problem, Numer. Math. 39 (1982), 269292. MR 669322

[L] O. E. Lanford III, Computer assisted proofs in analysis, Physica 124A (1984), 465470. 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), 417423. 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), 6571. MR 495314

[MP] R. MacKay and I. C. Percival, Converse K.A.M.: Theory and Practice, Comm. Math. Phys. 98 (1985), 469512. 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 nonexistence of invariant circles for areapreserving twist maps, Comm. Math. Phys. 117 (1988), 177189. MR 946999

[Z] E. Zehnder, Generalized implicit function theorems and applications to some small divisor problems, Comm. Pure Appl. Math. 28 (1975), 91140; 29 (1975), 49111. MR 380867
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DOI:
https://doi.org/10.1090/S027309791990158483