  Given a volume preserving dynamical system with non-compact phase space, one
is sometimes interested in special subsets of its wandering set. One example
from celestial mechanics is the set of initial values leading to collision.
Another one is the set of initial values of semi-orbits, whose asymptotic
velocity does not exist as a limit. We introduce techniques that can be helpful
in showing that these sets are of measure zero: by defining a sequence of
hypersurfaces, that are eventually hit by each of those semi-orbits and whose
total surface area decreases to zero.
