Searches for "Arnold Diffusion" and "Chaotic" Motion in the Beam-Bean Interaction

The results of long time computer simulation searches for "Arnold Diffusion" in beam-beam interactions at p¿p collider parameters are presented. No evidence of significant diffusion is found, consistent with beam storage for many days without "blow-up". "Chaotic" motion is observed in 2-D simulations at p¿p parameters by use of reversability tests, and Lyapunov exponents for the chaotic motion are measured. This motion appears at the intersections of low-order resonances. Chaotic motion in 1-D simulations and in simulations with tune modulation can also occur. The conditions for the appearance of chaotic motion are explored as well as its relationship with "beam blow-up".