Necessary and sufficient conditions on the weight family ensure strong continuity of the translation semigroup on directed metric trees, with hypercyclicity and weak mixing determined by the asymptotic decay of the weights along the tree.
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Dynamics of the translation semigroup on directed metric trees
Necessary and sufficient conditions on the weight family ensure strong continuity of the translation semigroup on directed metric trees, with hypercyclicity and weak mixing determined by the asymptotic decay of the weights along the tree.