  We study the thermodynamics and dynamics of high-dimensional
Einstein-power-Yang-Mills black holes in conformal gravity. Specifically, we
investigate a class of conformally related black holes whose metrics differ by
a scale factor. We show that a suitable scale factor cures the geodesic
incompleteness and the divergence of Kretschmann scalars at the origin of
spacetimes. In the aspect of thermodynamics, we analyse the Hawking
temperature, the entropy, and the specific heat, and verify the existence of
second-order phase transitions. We find that the thermodynamics of this class
of conformally related black holes is independent of scale factors. In the
aspect of dynamics, we find that the quasinormal modes of scalar field
perturbations are dependent on scale factors. Quite interesting is that the
behavior of quasinormal mode frequencies also supports the independence of
scale factors for the second-order phase transitions. Our results show that the
scale factors produce distinct thermodynamic and dynamic effects in the
conformally related Einstein-power-Yang-Mills black holes, which provides an
interesting connection between thermodynamics and dynamics of black holes in
conformal gravity.
