A Chaotic Linear Operator

2017. 03. 30. 10:15
BME H épület 306-os terem
Kiss Márton (BME Differenciálegyenletek Tanszék)

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 l2l2 displays chaotic dynamics. We give an outline of the proof starting from Devaney's definition of chaos. Then we construct the corresponding operator on the space of periodic functions and provide its representation involving a principal value integral. We explicitly calculate its eigenfunctions, as well as its periodic points; and also provide examples of chaotic and unbounded trajectories. Joint work with Tamás Kalmár-Nagy. (The talk will be in English.)

Related papers or presentations: paper1paper2