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Ergodicity and its applications. II: Averaging method of some dynamical systems. (English) Zbl 0973.37005

This paper is devoted to the role of ergodicity, more precisely of an ergodic function in the study of the averaging method. The author uses ergodicity ideas to show existence and uniqueness of generalized almost periodic solutions of some class of nonlinear differential equations containing a small parameter. The author presents some examples of this type of equations and provides examples where the averaging method fails if the function is not ergodic.

For Part I, cf. Acta Anal. Funct. Appl. 1, No. 1, 28-39 (1999; Zbl 0960.37002).

37A25Ergodicity, mixing, rates of mixing
34C29Averaging method
34E15Asymptotic singular perturbations, general theory (ODE)
34C27Almost and pseudo-almost periodic solutions of ODE