We show that most particle and subhalo orbits in simulated cosmological cold dark matter halos are surprisingly regular and periodic: The phase space structure of the outer halo regions shares some of the properties of the classical self-similar secondary infall model. Some of the outer branches are clearly visible in the radial velocity - radius plane at certain epochs. However, they are severely broadened in realistic, triaxial halos with non-radial, clumpy, mass accretion. This prevents the formation of high density caustics: Even in the best cases there are only broad, very small (<10 percent) enhancements in the spherical density profile. Larger fluctuations in rho(r) caused by massive satellites are common. Infall caustics are therefore too weak to affect lensing or dark matter annihilation experiments. Their detection is extremely challenging, as it requires a large number of accurate tracer positions and radial velocities in the outer halo. The stellar halo of the Milky Way is probably the only target where this could become feasible in the future.

5 pages, 3 figures, ApJL accepted. MPEG animations of Figures 1 and 2 are available at http://www.ucolick.org/~diemand/vl/movies.html#infall