  Dual-unitary circuits are being vigorously studied as models of many-body
quantum chaos that can be solved exactly for correlation functions and time
evolution of states. Here we define their classical counterparts as
dual-canonical transformations and associated dual-Koopman operators. Like
their quantum counterparts, the correlations vanish everywhere except on the
light cone, on which they decay with rates governed by a simple contractive
map. Providing a large class of such dual-canonical transformations, we study
in detail the example of a coupled standard map and show analytically that
arbitrarily away from the integrable case, in the thermodynamic limit the
system is mixing. We also define ``perfect" Koopman operators that lead to the
correlation vanishing everywhere including on the light cone and provide an
example of a cat-map lattice which would qualify to be a Bernoulli system at
the apex of the ergodic hierarchy.
