  We compute out-of-time-order correlators (OTOCs) in two-dimensional
holographic conformal field theories (CFTs) with different left- and
right-moving temperatures. Depending on whether the CFT lives on a spatial line
or circle, the dual bulk geometry is a boosted BTZ black brane or a rotating
BTZ black hole. In the case when the spatial direction is non-compact, we
generalise a computation of Roberts and Stanford and show that to reproduce the
correct bulk answer a maximal channel contribution needs to be selected when
using the identity block approximation. We use the correspondence between
global conformal blocks and geodesic Witten diagrams to extend our results to
CFTs on a spatial circle.
  In arXiv:1908.03574 it was shown that the OTOC for a rotating BTZ black hole
exhibits a periodic modulation about an average exponential decay with Lyapunov
exponent $2\pi/\beta$. In the extremal limit where the black hole is maximally
rotating, it was shown in arXiv:2009.08518 that the OTOC exhibits an average
cubic growth, on which is superposed a sawtooth pattern which has small periods
of Lyapunov growth due to the non-zero temperature of left-movers in the dual
CFT. Our computations explain these results from a dual CFT perspective.
