Necessary and sufficient conditions to be an eigenvalue for linearly   recurrent dynamical Cantor systems
  We give necessary and sufficient conditions to have measurable and continuous eigenfunctions for linearly recurrent Cantor dynamical systems. We also construct explicitly an example of linearly recurrent system with nontrivial Kronecker factor and a trivial maximal equicontinuous factor. 
Xavier Bressaud, Fabien Durand (LAMFA), Alejandro Maass (CMM)