  We resolve the isomorphism problem for tensor algebras of unital
multivariable dynamical systems. Specifically we show that unitary equivalence
after a conjugation for multivariable dynamical systems is a complete invariant
for complete isometric isomorphisms between their tensor algebras. In
particular, this settles a conjecture of Davidson and Kakariadis relating to
work of Arveson from the sixties, and extends related work of Kakariadis and
Katsoulis.
