The Minimal Center of Attraction of Measurable Systems and Their Discretizations*

A generalization of the Birkhoff minimal center of attraction is introduced and investigated for dynamical systems generated by single- and multi-valued Borel measurable mappings. In particular, it is shown to be equal to the minimal closed set containing the supports of the semi-invariant measures of the system. Its approximation under the spatial discretization of the state space is also considered.