Relevance of computer experiments to the pure mathematics of integrable and ergodic dynamical systems
Système dynamique I - Varsovie, Astérisque, no. 49 (1977), pp. 75-92. 
@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},
     series = {Ast\'erisque},
     pages = {75--92},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {49},
     year = {1977},
     mrnumber = {482844},
     zbl = {0374.28013},
     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
SP  - 75
EP  - 92
IS  - 49
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1977__49__75_0/
LA  - en
ID  - AST_1977__49__75_0
ER  - 
%0 Book Section
%A Ford, Joseph
%T Relevance of computer experiments to the pure mathematics of integrable and ergodic dynamical systems
%B Système dynamique I - Varsovie
%A Collectif
%S Astérisque
%D 1977
%P 75-92
%N 49
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1977__49__75_0/
%G en
%F AST_1977__49__75_0
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), pp. 75-92. 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 | Zbl

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

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

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 | Zbl

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

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

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

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

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

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

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 | Zbl

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

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

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

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 | Zbl

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

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

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

21. R. F. Williams, "The Structure of Lorenz Attractors," preprint, to appear. | DOI