  Differences in masses inferred from dynamics, such as velocity dispersions or
X-rays, and those inferred from lensing are a generic prediction of modified
gravity theories. Viable models however must include some non-linear mechanism
to restore General Relativity (GR) in dense environments, which is necessary to
pass Solar System constraints on precisely these deviations. In this paper, we
study the dynamics within virialized structures in the context of two modified
gravity models, f(R) gravity and DGP. The non-linear mechanisms to restore GR,
which f(R) and DGP implement in very different ways, have a strong impact on
the dynamics in bound objects; they leave distinctive signatures in the
dynamical mass-lensing mass relation as a function of mass and radius. We
present measurements from N-body simulations of f(R) and DGP, as well as
semi-analytical models which match the simulation results to surprising
accuracy in both cases. The semi-analytical models are useful for making the
connection to observations. Our results confirm that the environment- and
scale-dependence of the modified gravity effects have to be taken into account
when confronting gravity theories with observations of dynamics in galaxies and
clusters.
