Abstract A continuous linear operator on a Fréchet space $$\mathcal {X}$$ X is frequently hypercyclic if there exists vector x such that for any nonempty open subset $$U\subset \mathcal U ⊂ the set of $$n\in \mathbb {N}\cup \{0\}$$ n <m...

We study the dynamical behaviour of weighted shifts defined on sequence spaces a directed tree. In particular, we characterize their boundedness as well when they are hypercyclic, weakly mixing and mixing.

In an earlier paper we supplied indirect proof of the existence universal possible worlds that have topological property being hypercyclic, which means they can access every world in sequences approach arbitrarily closely to world. That states there are but it does not exhibit such a explicitly. We now explicitly construct two worlds. A continuous constructs with transreal co-ordinates directly...