This article is cited in 10 scientific papers (total in 10 papers)
The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems
I. N. Sergeev
Faculty of Mechanics and Mathematics, Moscow State University
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.
differential system, zeros of solutions, oscillation and wandering, characteristic exponents.
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Sbornik: Mathematics, 2013, 204:1, 114–132
Received: 02.09.2011 and 06.11.2012
I. N. Sergeev, “The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems”, Mat. Sb., 204:1 (2013), 119–138; Sb. Math., 204:1 (2013), 114–132
Citation in format AMSBIB
\paper The remarkable agreement between the oscillation and wandering characteristics of solutions of differential systems
\jour Mat. Sb.
\jour Sb. Math.
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A. Kh. Stash, “Existence of a two-dimensional linear system with continual spectra of total and vector frequencies”, Differ. Equ., 51:1 (2015), 146–148
I. N. Sergeev, “Polnyi nabor sootnoshenii mezhdu pokazatelyami koleblemosti, vraschaemosti i bluzhdaemosti reshenii differentsialnykh sistem”, Izv. IMI UdGU, 2015, no. 2(46), 171–183
I. N. Sergeev, “Oscillation, Rotation, and Wandering Exponents of Solutions of Differential Systems”, Math. Notes, 99:5 (2016), 729–746
I. N. Sergeev, “Lyapunov characteristics of oscillation, rotation, and wandering of solutions of differential systems”, J. Math. Sci. (N. Y.), 234:4 (2018), 497–522
A. Kh. Stash, “The absence of residual property for total hyper-frequencies of solutions to third order differential equations”, Moscow University Mathematics Bulletin, 72:2 (2017), 81–83
E. M. Shishlyannikov, “The existence of a two-dimensional bounded system with continual and coinciding spectra of frequencies and of wandering exponents”, Sb. Math., 209:12 (2018), 1812–1826
I. N. Sergeev, “Plane rotability exponents of a linear system of differential equations”, J. Math. Sci. (N. Y.), 244:2 (2020), 320–334
A. Kh. Stash, “Some properties of oscillation indicators of solutions to a two-dimensional system”, Moscow University Mathematics Bulletin, 74:5 (2019), 202–204
A. Kh. Stash, “Svoistva pokazatelei koleblemosti reshenii lineinykh avtonomnykh differentsialnykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 558–568
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