|Title: "On finite range repulsive systems of finitely many particles."|
We consider the dynamics of finite system
of spherical particles where a fraction of the kenetic energy may be lost
during collisions. We present a simple demonstration that the set of initial
condiguration leading to infinitely many collisions in finite time can
have positive measure, contrary to the hard collision (energy conservation)
case, in which this particular set is claimed to be empty. We also show
that after sufficient time a system will decouple into maximal substems.
This generalizes proofs that in the hard sphere case there can be at most
finitely many collisions for almost all initial configurations.
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