Hausdorff dimension of Markov invariant sets

摘要

One of the old questions about exceptional minimal sets of codimension-one C~2-foliations of compact manifolds reads (compare [La]): Is the Lebesgue measure |M| of any exceptional minimal set M equal to 0? The answer in general is still unknown. The class of Markov minimal sets was introduced by John Cantwell and Lawrence Conlon [CC] in the context of this question. Among the other results, they proved that |M | =0 if M is a Markov exceptional minimal set. The same result in the particular case of a Markov exceptional minimal set with holonomy generated by two maps defined on a common interval was obtained in [Mat].