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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.

 

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