  The simplest examples of chaotic maps are linear, area-preserving maps on the
circle, torus, or product of tori; respectively known as the Bernoulli map, the
cat map, and the recently introduced "spatiotemporal" cat map. We study
correlation functions in these maps. For the Bernoulli map, we compute the
correlation functions in a variety of ways: by direct computation of the
integral, through Fourier series, through symbolic dynamics, and through
periodic orbits. In relation to the more standard treatment in terms of
eigenfunctions of the Perron-Frobenius operator, some of these methods are
simpler and also extend to multipoint correlation functions. For the cat map,
we compute correlation functions through a Fourier expansion, review and expand
on a prior treatment of two-point functions by Crawford and Cary, and discuss
the limitations of shadowing. Finally, for the spatiotemporal cat map --
intended to be a model of many-body chaos -- we show that connected correlation
functions of local operators vanish.
