Degenerate dynamical systems

JOEL FRANCISCO SAAVEDRA ALVEAR, Ricardo Troncoso, Jorge Zanelli

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)4383-4390
Number of pages8
JournalJournal of Mathematical Physics
Volume42
Issue number9
DOIs
StatePublished - 1 Sep 2001

Fingerprint Dive into the research topics of 'Degenerate dynamical systems'. Together they form a unique fingerprint.

Cite this