Bulletin (New Series) of the American Mathematical Society

Accurate strategies for small divisor problems

R. de la Llave and David Rana

Full-text: Open access

Article information

Bull. Amer. Math. Soc. (N.S.), Volume 22, Number 1 (1990), 85-90.

First available in Project Euclid: 4 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39–04 39B99: None of the above, but in this section 70K50: Bifurcations and instability 58F27
Secondary: 65J15: Equations with nonlinear operators (do not use 65Hxx) 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX] 58F30 58F10


de la Llave, R.; Rana, David. Accurate strategies for small divisor problems. Bull. Amer. Math. Soc. (N.S.) 22 (1990), no. 1, 85--90. https://projecteuclid.org/euclid.bams/1183555458

Export citation


  • [A] V. I. Arnold, Geometric methods in the theory of ordinary differential equations, Springer-Verlag, Berlin and New York, 1983.
  • [CC] A. Celletti and L. Chierchia, Construction of analytic K.A.M. surfaces and effective stability bounds, Comm. Math. Phys. 118 (1988), 119-161.
  • [BZ] D. Braess and E. Zehnder, On the numerical treatment of a small divisor problem, Numer. Math. 39 (1982), 269-292.
  • [L] O. E. Lanford III, Computer assisted proofs in analysis, Physica 124A (1984), 465-470.
  • [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.
  • [M] R. E. Moore, Methods and applications of interval analysis, SIAM Philadelphia, 1979.
  • [Mo] J. Moser, Is the solar system stable?, Math. Intelligencer 1 (1978), 65-71.
  • [MP] R. MacKay and I. C. Percival, Converse K.A.M.: Theory and Practice, Comm. Math. Phys. 98 (1985), 469-512.
  • [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.
  • [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.