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Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems. (English) Zbl 1320.37027
The authors’ results from [Trans. Am. Math. Soc. 365, No. 10, 5329–5365 (2013; Zbl 1350.37061)], on what the authors call principal Lyapunov exponents and principal Floquet subspaces, are specialized for positive linear random dynamical systems on finite-dimensional ordered normed vector spaces. Conditions are given for systems generated by products of non-negative matrices and by strongly co-operative or by type-\(K\) strongly monotone linear differential equations to admit measurable families of generalized principal Floquet subspaces, generalized principal Lyapunov exponents, and generalized exponential splittings.

37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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