A dynamical system approach to the Kakutani-Fibonacci sequence
  In this paper we consider the sequence of Kakutani's $\alpha$-refinements corresponding to the inverse of golden ratio (which we call Kakutani-Fibonacci sequence of partitions) and associate to it an ergodic interval exchange (which we call Kakutani-Fibonacci transformation) using the "cutting-stacking" technique. We prove that the orbit of the origin under this map coincides with a low discrepancy sequence (which we call Kakutani-Fibonacci sequence of points), which has been also considered by other authors. 
Ingrid Carbone, Maria Rita Iac\`o, Aljo\v{s}a Vol\v{c}i\v{c}
math.DS math.NT