Volume 6, Number 4, Winter 1998
POINCARÉ'S STABILITY CONDITION
FOR QUASI-PERIODIC ORBITS
MICHAEL Y. LI AND JAMES S. MULDOWNEY
Abstract. A criterion for the orbital asymptotic stability
of a quasi-periodic solution to autonomous systems in any
finite dimension is derived. A principal tool used is the theory
of compound matrices and compound linear differential systems.
Results generalize a stability criterion of Poincaré for
periodic solutions of planar autonomous systems.