This article is cited in 7 papers

The existence of a two-dimensional bounded system with continual and coinciding spectra of frequencies and of wandering exponents

E. M. Shishlyannikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A two-dimensional linear homogeneous differential system with continuous bounded coefficients is constructed so that the frequencies and wandering exponents of each of its nonzero solutions coincide with each other and the set of their values at different solutions (the spectrum) is some interval of the number line.
Bibliography: 12 titles.

Keywords: linear system, characteristic exponents, frequencies, wandering exponents, uniformly distributed sequence.

UDC: 517.926

MSC: 34C10, 34D08

Received: 21.07.2017 and 14.07.2018

DOI: 10.4213/sm8995

 English version: Sbornik: Mathematics, 2018, 209:12, 1812–1826

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