Dynamics of linear operators connected with $\mathrm{su}(1,1)$ algebra
Vitaly Eduardovich Kim · Ufimskii Matematicheskii Zhurnal · 2014
In the present work we consider a linear continuous operator in a separable Fréchet space being one of the generators of Lie algebra su(1, 1).We study the discretetime dynamical system generated by iterations 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.