Relevance of computer experiments to the pure mathematics of integrable and ergodic dynamical systems
Système dynamique I - Varsovie, Astérisque, no. 49 (1977), 18 p. 
@incollection{AST_1977__49__75_0,
     author = {Ford, Joseph},
     title = {Relevance of computer experiments to the pure mathematics of integrable and ergodic dynamical systems},
     booktitle = {Syst\`eme dynamique I - Varsovie},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {49},
     year = {1977},
     zbl = {0374.28013},
     mrnumber = {482844},
     language = {en},
     url = {http://www.numdam.org/item/AST_1977__49__75_0/}
}
TY  - CHAP
AU  - Ford, Joseph
TI  - Relevance of computer experiments to the pure mathematics of integrable and ergodic dynamical systems
BT  - Système dynamique I - Varsovie
AU  - Collectif
T3  - Astérisque
PY  - 1977
DA  - 1977///
IS  - 49
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1977__49__75_0/
UR  - https://zbmath.org/?q=an%3A0374.28013
UR  - https://www.ams.org/mathscinet-getitem?mr=482844
LA  - en
ID  - AST_1977__49__75_0
ER  - 
Ford, Joseph. Relevance of computer experiments to the pure mathematics of integrable and ergodic dynamical systems, dans Système dynamique I - Varsovie, Astérisque, no. 49 (1977), 18 p. http://www.numdam.org/item/AST_1977__49__75_0/

1. M. Toda, Phys. Letters (Section C): Phys. Reports 18C, 1 (1975).

2. J. Moser, Adv. in Math. 16, 197 (1975) | MR 375869 | Zbl 0303.34019

B. A. Dubrovin, V. B. Mateev, and S. P. Novikov, Russ. Math. Surv. 31, 59 (1976). | Zbl 0346.35025

3. A. C. Scott, F. Y. F. Chu, and D. W. Mclaughlin, Proc. IEEE (USA) 61, 1443 (1973). | MR 358045

4. J. Ford, S. D. Stoddard, and J. S. Turner, Prog. Theor. Phys. 50, 1547 (1973).

5. V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (W. A. Benjamin, Inc., New York, 1968), Appendix 31. | MR 232910 | Zbl 0167.22901

6. C. L. Siegel, Ann. Math. 42, 806 (1941) | JFM 67.0768.01 | Zbl 0025.26503

C. L. Siegel ; Math. Ann 128, 144 (1954). | MR 67298

7. F. G. Gustavson, Astron J. 71, 670 (1966).

8. G. H. Lunsford and J. Ford, J. Math. Phys. 13, 700 (1972). | MR 305762 | Zbl 0241.34044

9. M. Henon, Phys. Rev. B9, 1921 (1974). | MR 408646 | Zbl 0942.37503

10. H. Flaschka, Phys. Rev. B9, 1924 (1974). | Zbl 0942.37504

11. A third, independent, rigorous proof has also been given by S. V. Manakov, Soviet Phys.-JETP 40, 269 (1974).

The general solution to the Toda lattice has been given by M. Kac and P. Van Moerbeke, Proc. Nat. Acad. Sci. USA 72, 2879 (1975) | MR 426538 | Zbl 0343.34004

The general solution to the Toda lattice has been given by E. Date and S. Tanaka, Prog. Theor. Phys. 55, 457 (1976). | MR 403367 | Zbl 1109.37307

For a survey of recent developments, see Progress of Theoretical Physics Supplement No. 59, 1976.

12. M. Henon and C. Heiles, Astron J. 69, 73 (1964). | MR 158746

13. See Ch. 3 of Ref. 5.

14. See pp. 92-93 of Ref. 5.

15. See Ch. 4 of Ref. 5.

16. Ya. G. Sinai, Russ. Math. Surv. 25, 137 (1970). | Zbl 0263.58011

17. G. Benettin and J. M. Strelcyn, "Numerical Experiments on the Free Motion of a Point Mass Moving in a Plane Convex Region : Stochastic Transition and Entropy for the Billiard," Phys. Rev. A, to appear.

18. M. Henon, Commun. Math. Phys. 50, 69 (1976). | MR 422932 | Zbl 0576.58018

19. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963).

20. D. Ruelle and F. Takens, Commun. Math, Phys. 20, 167 | MR 284067

D. Ruelle and F. Takens, Commun. Math, Phys. 23, 343 (1971). | MR 292391 | Zbl 0227.76084

21. R. F. Williams, "The Structure of Lorenz Attractors," preprint, to appear. | Article | MR 461581 | Zbl 0484.58021