@incollection{Farkas2005,
  author    = {{Hershel M. Farkas}},
  title     = {{Variants of the $3N+1$ problem and multiplicative semigroups}},
  booktitle = {{Geometry, Spectral Theory, Groups and Dynamics: Proceedings in Memory of Robert Brooks}},
  publisher = {{Amer. Math. Soc., Providence}},
  year      = {{2005}},
  volume    = {{387}},
  pages     = {{121--127}},
  note      = {{MR 2006g:11052}},
}