  Motivated by the recent connection between pole-skipping phenomena of two
point functions and four point out-of-time-order correlators (OTOCs), we study
the pole structure of thermal two-point functions in $d$-dimensional conformal
field theories (CFTs) in hyperbolic space. We derive the pole-skipping points
of two-point functions of scalar and vector fields by three methods (one field
theoretic and two holographic methods) and confirm that they agree. We show
that the leading pole-skipping point of two point functions is related with the
late time behavior of conformal blocks and shadow conformal blocks in
four-point OTOCs.
