Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions

Abstract EN

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 l2 displays chaotic dynamics.

Here we construct the corresponding operator C on the space of 2π-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 C.