Behavior of conditional stability under a change of the parameters

The author proves that the lower semicontinuity with respect to the parameter of certain functions arising in the consideration of families of differential equations is typical (in the Baire category sense). In the case considered these functions are level sets of Lyapunov exponents of points of the space of a metric vector bundle with respect to a given family of endomorphisms. In this case a level set of a function is defined as the set of values of the arguments such that the function is less than a given number. The problem considered in the paper covers many concrete situations.
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