Let $(M,\omega)$ and $(M^{\prime},\omega^{\prime})$ are two symplectic manifolds. Then we may define a natural homotopy equivalence as follows.
We say that the smooth map $f:M\longrightarrow M^{\prime}$ is $\textbf{symplectic}$, if $f^{*}\omega^{\prime}=\omega$.
$\textbf{Definition}$: We say that the symplectic map $f:(M,\omega)\longrightarrow (M^{\prime},\omega^{\prime})$ is a symplectic homotopy equivalence, if there exists a symplectic map $g:(M^{\prime},\omega^{\prime})\longrightarrow (M,\omega)$ such that $g\circ f\simeq id_{M}$ and $f\circ g\simeq id_{M^{\prime}}$.
I want to search some papers that consider such symplectic homotopy equivalence, can somebody help me?