Category and compact leaves

We prove that if F is a C 1 –foliation of a compact manifold M with finite transverse saturated LS category, cat s ( M , F ) < ∞ , then F has a compact leaf. In contrast, we show that if F is expansive on some non-trivial minimal set of F , then cat s ( M , F ) = ∞ . Examples of foliations are given to illustrate the main results of the paper.