  $\rm Yb_2Ti_2O_7$ is a celebrated example of a pyrochlore magnet with
highly-frustrated, anisotropic exchange interactions. To date, attention has
largely focused on its unusual, static properties, many of which can be
understood as coming from the competition between different types of magnetic
order. Here we use inelastic neutron scattering with exceptionally high energy
resolution to explore the dynamical properties of $\rm Yb_2Ti_2O_7$. We find
that spin correlations exhibit dynamical scaling, analogous to behavior found
near to a quantum critical point. We show that the observed scaling collapse
can be explained within a phenomenological theory of multiple--phase
competition, and confirm that a scaling collapse is also seen in
semi--classical simulations of a microscopic model of $\rm Yb_2Ti_2O_7$. These
results suggest a general picture for dynamics in systems with competing ground
states.
