Dynamics of linear operators connected with $\mathrm{su}(1,1)$ algebra

In the present work we consider a linear continuous operator in a separable Frechet space being one of the generators of Lie algebra $\mathrm{su}(1,1)$. We study the discrete-time dynamical system generated by iteration of this operator. We show that under some additional conditions the operator that generates the indicated dynamical system is frequently hypercyclic and chaotic (in the sense of Devaney). Applications of this result to a study of specific operators are indicated.