How do topological entropy of a flow and entropy of Poincare map relate?

Question

I’m trying to study some properties of topological entropy of flows. I’m using that given a flow $\phi_t$, its topological entropy is equal to $h(\phi_1)$, and I found that $h(\phi_t)=|t|h(\phi_1)$. But I’m interested in what the Poincare map gives on entropy. Assuming that there is a global section, and defining the first return map $P$, how do $h(P)$ and $h(\phi_1)$ relate? I think it should be something like $a h(\phi_1)\leq h(P) \leq b h(\phi_1)$, where $a$ and $b$ are the minimum and maximum times of return, but I can’t find anything about it.