On sets of linear differential systems to which perturbed linear systems cannot be reduced View Full Text


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Article Info

DATE

2011-11

AUTHORS

N. A. Izobov, S. A. Mazanik

ABSTRACT

The paper [2] defines the noncoinciding irreducibility sets N2(a, σ) and N3(a, σ), σ ∈ (0, 2a], of all n-dimensional linear differential systems with piecewise continuous coefficient matrices A(t) such that ‖A(t)‖ ≤ a < + ∞ for t ∈ [0,+∞) and there exists a linear differential system that is not Lyapunov reducible to the original system and has coefficient matrix B(t) satisfying [for the case of N2(a, σ)] the condition or [for the case of N3(a, σ)] the more general condition that the Lyapunov exponent of the difference B(t) − A(t) does not exceed −σ. For these sets, which are related by the obvious inclusions , we prove that (i) they strictly decrease with increasing parameter σ ∈ (0, 2a], Ni(a, σ1) ⊃ Ni(a, σ2) for σ1 < σ2; (ii) there is a strict inclusion N2(a, σ) ⊂ N3(a, σ) for all σ ∈ (0, 2a]. More... »

PAGES

1563-1568

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0012266111110036

DOI

http://dx.doi.org/10.1134/s0012266111110036

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018160309


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