  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 center of black
holes. 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 minimally coupled 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.
