A weighted backward shift on ℓ^p or c0 spaces over a directed tree is chain recurrent iff the weights meet forward divergence on each vertex's descendants and, for unrooted trees, backward divergence on ancestors.
Grosse-Erdmann and Dimitris Papathanasiou
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Chain recurrent shifts on trees
A weighted backward shift on ℓ^p or c0 spaces over a directed tree is chain recurrent iff the weights meet forward divergence on each vertex's descendants and, for unrooted trees, backward divergence on ancestors.