Qualitative theory and expansion growth of transversely piecewise-smooth foliated ${S}^{1}$-bundles

Abstract

We study a qualitative theory of compact, transversely piecewise-smooth foliated $S^1$-bundles. We show that it has the same qualitative properties as that of smooth codimension-one foliations on a compact manifold. By the obtained qualitative properties, we can deduce that the expansion growth of this foliation is classified and that the entropy of this foliation is positive if and only if there exists a resilient leaf.