Foliations I, Authors Alberto Candel and Lawrence Conlon, Chapter $12$, Page $320$, Corollary $12.2.32$.
Let $(M,\mathcal{F},\pi,B,F)$ be a $C^2-$ Foliated Bundle with a Fibre $F$ compact Metric Space, base $B$ Compact Manifold, and Total Holonomy Hroup $\Gamma_{\mathcal{F}}$. Let $L$ be a Leaf of $\mathcal{F}$ corresponding to the orbit $\Gamma_{\mathcal{F}}(x)$, $x\in F$. Then $gr(L)=gr(\Gamma_{\mathcal{F}}(x))$.
By $gr(L)$, we mean the Growth Type of the Growth Function of the Leaf $L$.
By $gr(\Gamma_{\mathcal{F}}(x))$, we mean the Growth Type of the Growth Function of the Orbit $\Gamma_{\mathcal{F}}(x)$.
What do they exactly mean by saying (Let $L$ be a leaf of $\mathcal{F}$ corresponding to the orbit $\Gamma_{\mathcal{F}}(x)$, $x\in F$)?
What is the correspondence between the leaves of the foliation and the orbits?
