periodic orbits & more

dynamical systems studies *interesting* behaviors in systems. one such class of interesting behaviors is equilibria, with stable and unstable varieties. but there’s more. consider a slight variation on the shaken inverted pendulum, where the shaking is happening horizontally. this leads to interesting and varied behaviors, depending (somewhat sensitively) on the initial conditions. some are *periodic* (they repeat over time); others seem to keep evolving and keep getting more & more complex. what is happening? how do we make sense of such? oh, there’s much more to learn about dynamical systems…