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We propose a general exact method of calculating dynamical correlationfunctions in dual symplectic brick-wall circuits in one dimension. These aredeterministic classical many-body dynamical systems which can be interpreted interms of symplectic dynamics in two orthogonal (time and space) directions. Inclose analogy with quantum dual-unitary circuits, we prove that two-pointdynamical correlation functions are non-vanishing only along the edges of thelight cones. The dynamical correlations are exactly computable in terms of aone-site Markov transfer operator, which is generally of infinitedimensionality. We test our theory in a specific family of dual-symplecticcircuits, describing the dynamics of a classical Floquet spin chain.Remarkably, expressing these models in the form of a composition of rotationsleads to a transfer operator with a block diagonal form in the basis ofspherical harmonics. This allows us to obtain analytical predictions for simplelocal observables. We demonstrate the validity of our theory by comparison withMonte Carlo simulations, displaying excellent agreement with the latter fordifferent choices of observables.

Dual symplectic classical circuits: An exactly solvable model of many-body chaos