  We study two problems related to flow equivalence of shift spaces. The first
problem, the classification of $S$-gap shifts up to flow equivalence, is
partially solved with the establishment of a new invariant for the sofic
$S$-gap shifts and a complete classification of the non-sofic $S$-gap shifts.
The second problem is an examination of the entropy of shift spaces under flow
equivalence. For a wide array of classes of shift spaces with non-zero entropy,
it is shown that the entropies achievable while maintaining flow equivalence
are dense in $\mathbb R^+$.
