Abstract
For exponential dichotomies defined by nonautonomous linear equations, we show that sufficiently small C 1 -parameterized perturbations originate a family of exponential dichotomies of class C 1 in the parameter. We consider the general case of nonuniform exponential dichotomies, and also the general case of arbitrary growth rates of the form e λ ρ ( t ) where ρ is an arbitrary function. This includes the usual exponential behavior as a very special case when ρ ( t ) = t .
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