A canonical system of two differential equations with periodic coefficients and the Poincar,-Denjoy theory of differential equations on a torus

作者：Perov A I^*

来源：Siberian Mathematical Journal, 2010, 51(2): 301-312.

DOI：10.1007/s11202-010-0031-6

• canonical system
• Floquet multiplier
• domains of strong stability
• Poincare-Denjoy theory
• rotation number

The passage from Cartesian to polar coordinates in a canonical system with periodic coefficients gives rise to a nonlinear differential equation whose right-hand side is periodic in time and the polar angle and thus this equation can be regarded as a differential equation on a torus. In accord with Poincar,-Denjoy theory, the behavior of a solution to a differential equation on a torus is characterized by the rotation number and some homeomorphic mapping of a circle onto itself. We study connections of strong stability (instability) of a canonical system, including the membership in the nth stability (instability) domain, with the rotation number and fixed points of this mapping.

• 出版日期2010-3