TY - JOUR

T1 - Degenerate dynamical systems

AU - Saavedra, Joel

AU - Troncoso, Ricardo

AU - Zanelli, Jorge

PY - 2001/9

Y1 - 2001/9

N2 - Dynamical systems, whose symplectic structure degenerates, becoming noninvertible 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 mechanics, the degeneracy occurs on domain walls that divide phase space into nonoverlapping 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 orbits. In this latter case, once the system reaches the domain wall, it acquires a new gauge invariance and one degree of freedom is dynamically frozen, while the remaining degrees of freedom evolve regularly thereafter.

AB - Dynamical systems, whose symplectic structure degenerates, becoming noninvertible 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 mechanics, the degeneracy occurs on domain walls that divide phase space into nonoverlapping 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 orbits. In this latter case, once the system reaches the domain wall, it acquires a new gauge invariance and one degree of freedom is dynamically frozen, while the remaining degrees of freedom evolve regularly thereafter.

UR - http://www.scopus.com/inward/record.url?scp=0035537188&partnerID=8YFLogxK

U2 - 10.1063/1.1389088

DO - 10.1063/1.1389088

M3 - Article

AN - SCOPUS:0035537188

SN - 0022-2488

VL - 42

SP - 4383

EP - 4390

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 9

ER -