The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems

Journal Article · Thu Jan 31 00:00:00 EST 2013 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2013V204N01ABEH004293· OSTI ID:22156563

Sergeev, Igor N ^[1]

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1. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

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. Bibliography: 17 titles.

• OSTI ID: 22156563
• Journal Information: Sbornik. Mathematics, Vol. 204, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ANGULAR VELOCITY
DIFFERENTIAL EQUATIONS
LYAPUNOV METHOD
MATHEMATICAL SOLUTIONS
OSCILLATIONS
ROTATION