Bulletin (New Series) of the American Mathematical Society

A computer-assisted proof of the Feigenbaum conjectures

Oscar E. Lanford

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.) Volume 6, Number 3 (1982), 427-434.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.bams/1183548786

Mathematical Reviews number (MathSciNet)
MR648529

Zentralblatt MATH identifier
0487.58017

Subjects
Primary: 58F14

Citation

Lanford, Oscar E. A computer-assisted proof of the Feigenbaum conjectures. Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 427--434. http://projecteuclid.org/euclid.bams/1183548786.


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References

  • 1. M. Campanino, H. Epstein and D. Ruelle, On Feigenbaum's functional equation, (IHES preprint P/80/32 (1980)) Topology (to appear).
  • 2. M. Campanino and H. Epstein, On the existence of Feigenbaum's fixed point, (IHES preprint P/80/35 (1980)) Comm. Math. Phys. (1981), 261-302.
  • 3. P. Collet and J. P. Eckmann, Iterated maps of the interval as dynamical systems, Birkhäuser, Boston-Basel-Stuttgart, 1980.
  • 4. P. Collet, J. P. Eckmann and O. E. Lanford, Universal properties of maps on an interval, Comm. Math. Phys. 76 (1980), 211-254.
  • 5. M. Feigenbaum, Quantitative universality for a class of non-linear transformations, J. Statist. Phys. 19 (1978), 25-52.
  • 6. M. Feigenbaum, The universal metric properties of non-linear transformations, J. Statist. Phys. 21 (1979), 669-706.
  • 7. O. E. Lanford, Remarks on the accumulation of period-doubling bifurcations. Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, vol. 116, Springer-Verlag, Berlin and New York, 1980, pp. 340-342.
  • 8. O. E. Lanford, Smooth transformations of intervals, Séminaire Bourbaki, 1980/81, No. 563, Lecture Notes in Math., vol. 901, Springer-Verlag, Berlin, Heidelberg and New York, 1981, pp. 36-54.