The use of ergodic theory in designing dynamics for search problems

In this paper, we use tools from ergodic theory to design dynamics for searching for a target of unknown size. We show that the expected time to find a target is controlled by the local dimension of the invariant measure. The expected time to find the target behaves as -C log δ where δ is the minimum volume of the target. This relation holds in any dimension for a large class of systems. Sampling non-uniform target priors and continuous time search are discussed.