Aperiodic Sequences and Aperiodic Geodesics
  We introduce a quantitative condition on orbits of dynamical systems which measures their aperiodicity. We show the existence of sequences in the Bernoulli-shift and geodesics on closed hyperbolic manifolds which are as aperiodic as possible with respect to this condition. 
Viktor Schroeder and Steffen Weil
math.DS math.DG math.MG