I have started reading the following paper arXiv link on Dynamical Systems and Symplectic Geometry and in page $3$ we have the following statement :

Let $\Sigma$ be a fiberwise starshaped Hypersurface in $T^*M$ and $H:T^*M\rightarrow \mathbb{R}$ such that $\sigma=H^{-1}(1)$ and $1$ is a regular value.Then the orbits of $\phi_H^t|_{\Sigma}$ do not depend on the choice of choice of $H$, in the sense that if we pick another $G$ such that $\Sigma=G^{-1}(1)$ and such that $1$ is a regular value, then the flow $\phi_G^t|_{\Sigma}$ is a time change of the flow of $\phi_{H}^t|_{\Sigma}$, i.e , there exists a smooth positive function $\sigma(t,x):\mathbb{R}\times \Sigma\rightarrow \mathbb{R}$ such that $\phi_G^t|_{\Sigma}=\phi_H^{\sigma(t,x)}|_{\Sigma}$.

Does anyone know a reference where I could check why this is true ? I have been thinking about this for a while and can't seem to come up with a proof myself.

Any help is appreciated. Thanks in advance.