Piecewise conjugacy for multivariable dynamics over the Jacobson spectrum of a C*-algebra

We show that if (A,a) and (B,b) are automorphic multivariable C*-dynamical systems with isometrically isomorphic tensor algebras (or semi crossed products), then the systems are piecewise conjugate over their Jacobson spectrum. This answers a question of Kakariadis and the author.