Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd -Periodic Functions

Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequences displays chaotic dynamics. Here we construct the corresponding operator on the space of -periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories of .

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