The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems
Sbornik: Mathematics, 204 (1):
114 (January 2013)DOI: 10.1070/SM2013v204n01ABEH004293
Abstract
Lyapunov-type oscillation and wandering indicators are defined for solutions of systems of differential equations; these are the average frequency of zeros for the projection of a solution onto some line and the average angular velocity of rotation of a solution about the origin in some basis, respectively. An integral equality relating these indicators is obtained. The indicators introduced are shown to coincide if, prior to averaging, the oscillation indicators are minimized over all possible lines, and the wandering indicators over all possible bases.