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Mat. Sb., 2013, Volume 204, Number 1, Pages 119–138 (Mi msb7928)  

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

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.
Bibliography: 17 titles.

Keywords: differential system, zeros of solutions, oscillation and wandering, characteristic exponents.

DOI: https://doi.org/10.4213/sm7928

Full text: PDF file (547 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:1, 114–132

Bibliographic databases:

UDC: 517.926
MSC: 34C10
Received: 02.09.2011 and 06.11.2012

Citation: 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
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. N. Sergeev, “Turnability characteristics of solutions of differential systems”, Differ. Equ., 50:10 (2014), 1342–1351  crossref  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
    2. 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  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. I. N. Sergeev, “Polnyi nabor sootnoshenii mezhdu pokazatelyami koleblemosti, vraschaemosti i bluzhdaemosti reshenii differentsialnykh sistem”, Izv. IMI UdGU, 2015, no. 2(46), 171–183  mathnet  elib
    4. I. N. Sergeev, “Oscillation, Rotation, and Wandering Exponents of Solutions of Differential Systems”, Math. Notes, 99:5 (2016), 729–746  mathnet  crossref  crossref  mathscinet  isi  elib
    5. 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  mathnet  crossref
    6. 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  mathnet  crossref  mathscinet  isi
    7. 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  mathnet  crossref  crossref  adsnasa  isi  elib
    8. I. N. Sergeev, “Plane rotability exponents of a linear system of differential equations”, J. Math. Sci. (N. Y.), 244:2 (2020), 320–334  mathnet  crossref  elib
    9. A. Kh. Stash, “Some properties of oscillation indicators of solutions to a two-dimensional system”, Moscow University Mathematics Bulletin, 74:5 (2019), 202–204  mathnet  crossref  mathscinet  isi
    10. A. Kh. Stash, “Svoistva pokazatelei koleblemosti reshenii lineinykh avtonomnykh differentsialnykh sistem”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:4 (2019), 558–568  mathnet  crossref
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