Foliations and subshifts (Q1107174)

Local minimal sets (LMS) play an important role in the structure theory of compact, \(C^ 2\)-foliated manifolds of codimension one. A major gap in the theory concerns what are called exceptional LMS. For the case of Markov LMS, the following result is obtained: If X is a Markov LMS, then X contains only finitely many semiproper leaves and Lebesgue measure \(| X| =0\). The authors also give examples of LMS that are not Markov.