Forced oscillations.

Abstract

For f: J₀→ C ^m, we say that f is periodic if, for some positive integer τ,

$$f\left( {n + \tau } \right) = f\left( n \right)foral\ln \in {J_0};$$

τ is called a period of f. The least such τ is the least period. If τ is the least period, then the only periods of f are integral multiples of τ. For instance ${e^{i\frac{{2\Pi \sigma n}}{\tau }}}$,σ a nonnegative integer, is periodic of period τ.If (σ, τ) = 1, τ is the least period. The constant functions have period 1.