Collisions are of first category
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- by Donald G. Saari PDF
- Proc. Amer. Math. Soc. 47 (1975), 442-445 Request permission
Abstract:
It is shown that the set of initial conditions leading to collisions in the $n$-body problem of Newtonian mechanics is of (Baire) first category.References
- John E. Littlewood, Some problems in real and complex analysis, D. C. Heath and Company Raytheon Education Company, Lexington, Mass., 1968. MR 0244463
- Harry Pollard and Donald G. Saari, Singularities of the $n$-body problem. I, Arch. Rational Mech. Anal. 30 (1968), 263–269. MR 231565, DOI 10.1007/BF00281534
- Donald Gene Saari, Improbability of collisions in Newtonian gravitational systems, Trans. Amer. Math. Soc. 162 (1971), 267–271; erratum, ibid. 168 (1972), 521. MR 295648, DOI 10.1090/S0002-9947-1971-0295648-8
- Donald G. Saari, Improbability of collisions in Newtonian gravitational systems. II, Trans. Amer. Math. Soc. 181 (1973), 351–368. MR 321386, DOI 10.1090/S0002-9947-1973-0321386-0
- Donald G. Saari, Singularities and collisions of Newtonian gravitational systems, Arch. Rational Mech. Anal. 49 (1972/73), 311–320. MR 339596, DOI 10.1007/BF00250511
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 442-445
- MSC: Primary 70.58
- DOI: https://doi.org/10.1090/S0002-9939-1975-0366147-9
- MathSciNet review: 0366147