  In this article, we demonstrate how a 3-point correlation function can
capture the out-of-time-ordered features of a higher point correlation
function, in the context of a conformal field theory (CFT) with a boundary, in
two dimensions. Our general analyses of the analytic structures are independent
of the details of the CFT and the operators, however, to demonstrate a Lyapunov
growth we focus on the Virasoro identity block in large-c CFT's. Motivated by
this, we also show that the phenomenon of pole-skipping is present in a 2-point
correlation function in a two-dimensional CFT with a boundary. This
pole-skipping is related, by an analytic continuation, to the maximal Lyapunov
exponent for maximally chaotic systems. Our results hint that, the dynamical
content of higher point correlation functions, in certain cases, may be
encrypted within low-point correlation functions, and analytic properties
thereof.
