Аннотация:The presence of a discrete rational component in the spectrum of an ergodic automorphism S is inconsistent with the existence of certain roots of S. If T is an ergodic automorphism ofa space with σ-finite measure, then the discrete spectrum disappears from the product S ⊗ T , but thememory of it may remain in the form of the absence of roots, like Cheshire Cat’s grin. Under certainadditional assumptions, this effect is inherited by the Poisson suspension over such a product. Basedon this idea, we propose a simple rank-one construction for which the Poisson suspension has noroots and is rigid.
