## Dynamical System State Need Not Have SpectrumS. Boyd and L. O. Chua
Recently there has been much study of nonlinear dynamical systems (differential equations) which have chaotic solutions. While there is not precise definition of what a chaotic solution is, it is generally agreed upon that a chaotic trajectory should have a continuous spectrum, in particular, it should not be almost periodic. A natural question is, therefore, does a (bounded) trajectory of a dynamical system always have a spectrum? In this short note we give a simple example which shows that it need not. |