On the Difference in Cardinalities of the Spectra of Exact andAbsolute Wandering Indicators Between a Two-Dimensional Nonlinear System and the FirstApproximation System

The paper studies the spectra (sets of values) of wandering indicators of solutions of differential systems. We construct two-dimensional systems with a nonlinearity of a given arbitrarily high order of smallness in a neighborhood of the origin such that Moreover, these nonlinear two-dimensional systems have the same spectra of wandering indicators as their restrictions to the direct product of any open neighborhood of zero on the phase plane by the time half-line.