It is known that weakly chaotic dynamics, such as the type generated by Pomeau-Manneville intermittency maps, may lead to anomalous diffusion (Levy processes).  I will describe work in progress with Georg Gottwald indicating that when analysed in the context of systems with Euclidean E(n) symmetry, typically the anomalous diffusion persists if and only if n is odd.
In even dimensions, the anomalous diffusion is typically suppressed and replaced by Brownian motion.