  In this paper we continue investigating connections between Floer theory and
dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows.
Barcode entropy is the exponential growth rate of the number of not-too-short
bars in the Floer or symplectic homology persistence module. The key novel
result is that the barcode entropy is bounded from below by the topological
entropy of any hyperbolic invariant set. This, combined with the fact that the
topological entropy bounds the barcode entropy from above, established by
Fender, Lee and Sohn, implies that in dimension three the two types of entropy
agree. The main new ingredient of the proof is a variant of the Crossing Energy
Theorem for Reeb flows.
