Supremum of the Perron Exponent on the Solutions of a Linear System with Slowly Growing Coefficients is Metrically Typical

Abstract

We prove that if the Lyapunov exponent of the norm of the coefficient matrix of a linear differential system is nonpositive, then the supremum of Perron exponents of the solutions issuing from any given affine subspace is attained and the set of initial vectors of solutions with the maximum Perron exponent has full Lebesgue measure in the subspace.