Once more on quasiperiodic solutions of quasiperiodic dynamical systems. (Italian. English summary) Zbl 0727.34035

Manfredi, Bianca

Riv. Mat. Univ. Parma, IV. Ser. 16, 97-103 (1990).

Summary: After introducing the notion of “normal function with respect to a set of numbers” we show first that every normal solution with respect to the set \(\{\tau \}^+_{\epsilon_ 1f}\) of the positive \(\epsilon\)- quasiperiods of a given dynamic quasiperiodic system is asymptotically quasiperiodic, and conversely. Moreover we prove that every normal solution with respect to \(\{\tau \}^+_{\epsilon_ 1f}\) is always related to a quasiperiodic solution of a given dynamic quasiperiodic system.

MSC:

34C27

Almost and pseudo-almost periodic solutions to ordinary differential equations

Keywords:

normal function with respect to a set of numbers; dynamic quasiperiodic system; asymptotically quasiperiodic