Noncommutative topological entropy of endomorphisms of Cuntz algebras

Noncommutative topological entropy estimates are obtained for polynomial gauge invariant endomorphisms of Cuntz algebras, generalising known results for the canonical shift endomorphisms. Exact values for the entropy are computed for a class of permutative endomorphisms related to branching function systems introduced and studied by Bratteli, Jorgensen and Kawamura