Improbability of collisions in Newtonian gravitational systems. II

Author:
Donald G. Saari

Journal:
Trans. Amer. Math. Soc. **181** (1973), 351-368

MSC:
Primary 70.28

DOI:
https://doi.org/10.1090/S0002-9947-1973-0321386-0

MathSciNet review:
0321386

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Abstract: It is shown that the set of initial conditions leading to collision in the inverse square force law has measure zero. For the inverse force law the behavior of binary collisions for and the behavior of any collision for is developed. This information is used to show that collisions are improbable in the inverse force law where and that binary collisions are improbable for .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0321386-0

Keywords:
-body problem,
gravitational systems,
collision,
measure preserving,
singularities,
celestial mechanics

Article copyright:
© Copyright 1973
American Mathematical Society