On Riemann surfaces, pseudo-Anosov maps constitute the majority of the mapping class group and these maps display many interesting dynamical properties. One way to generate pseudo-Anosov maps is by compositions of Dehn twists. In this talk, I’ll show that on symplectic manifolds, we can also compose symplectic Dehn twists to obtain maps that display hyperbolic properties including positive topological entropy, stable and unstable laminations, and exponential growth of the Floer homology group. This represents joint work with Wenmin Gong and Jinxin Xue.