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In this paper, we study the hypercyclicity of forward and backward shifts onweighted $L^p$ spaces of a directed tree. In the forward case, only the trivialtrees may support hypercyclic shifts, in which case the classical results ofSalas apply. For the backward case, nontrivial trees may support hypercyclicshifts. We obtain necessary conditions and sufficient conditions forhypercyclicity of the backward shift and, in the case of a rooted tree on anunweighted space, we show that these conditions coincide.

Hypercyclicity of Shifts on Weighted ${\mathbf L}^p$ Spaces of Directed Trees