This paper shows that the general homogeneous solution to equations of evolution for some infinite systems of particles subject to mutual binary collisions does not depend on a single arbitrary constant but on a potentially infinite number of such constants. This is because, as I demonstrate, a single self-excitation of a system of particles can depend on a potentially infinite number of parameters. The recent homogeneous solution obtained by Atkinson and Johnson, which depends on a single arbitrary constant, is only a particular case.
Supertasks Colliding balls Infinite systems
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Atkinson, D.: Losing energy in classical, relativistic and quantum mechanics. Stud. Hist. Philos. Mod. Phys. 38, 170–180 (2007)CrossRefzbMATHGoogle Scholar