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1986 | OriginalPaper | Chapter

Forced oscillations.

Author : J. P. LaSalle

Published in: The Stability and Control of Discrete Processes

Publisher: Springer New York

Included in: Professional Book Archive

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For f: J₀→ Cm, 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.

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