Interpolation property for hypercyclic elements of the Taylor Shift operator

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In this article we deal with the hypercyclic complex Taylor shift operator acting on the space of holomorphic functions in a suitable simply connected domain, along with the real Taylor shift on the space of real infinitely differentiable functions. In both cases, we investigate a problem of interpolation for the class of hypercyclic elements. Further, we study the notion of disjoint hypercyclicity for subsequences of the orbit of the real Taylor shift.