Motivated by recent results in arithmetic dynamics, we will introduce a new invariant attached to a rational map f defined over the complex numbers. Its construction depends on an auxiliary equivariant -- a function on real hyperbolic 3 space -- which also appears to carry information about the dynamics of the map f. In this talk, we will discuss what is known about these objects, both in the setting of complex dynamics and in the setting of arithmetic dynamics. Speaker(s): Kenneth Jacobs (Northwestern)