Geodesic
On the existence of a~linear differential system with given values of the Perron exponent
Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 214-231.

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We consider linear differential systems with infinitely differentiable and, in general, unbounded coefficients on the semi-axis. We prove that the map assigning to a non-zero solution of such a system the value of the Perron exponent on the solution can turn out to be an arbitrary continuous function which is constant along every line passing through zero in the solution space.
Keywords: differential equation, linear system, Lyapunov exponents, Perron exponents. 
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A. Gargyants. On the existence of a~linear differential system with given values of the Perron exponent. Izvestiya. Mathematics , Tome 83 (2019) no. 2, pp. 214-231. http://geodesic.mathdoc.fr/item/IM2_2019_83_2_a2/

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