Dynamical systems, whose symplectic structure degenerates, becoming noninve
rtible at some points along the orbits, are analyzed. It is shown that for
systems with a finite number of degrees of freedom, like in classical mecha
nics, the degeneracy occurs on domain walls that divide phase space into no
noverlapping regions, each one describing a nondegenerate system, causally
disconnected from each other. These surfaces are characterized by the sign
of the Liouville flux density on them, behaving as sources or sinks of orbi
ts. In this latter case, once the system reaches the domain wall, it acquir
es a new gauge invariance and one degree of freedom is dynamically frozen,
while the remaining degrees of freedom evolve regularly thereafter. (C) 200
1 American Institute of Physics.