Strange attractors are a by now well-known phenomenon in chaotic dynamical systems. Although not the only of its kind, Hénon attractor is a standard and extensively studied component of chaotic dynamics. Despite being the center of intensive research for over three decades, the Hénon and other horseshoe-like strange attractors are still poorly understood.
An inverse limit space with a single bonding map can be seen as the collection of all backward orbits of a dynamical system of the bonding map. Unimodal inverse limits model (to some extend) the Hénon-like attractors, but they are also sufficiently complicated themselves to leave us with many questions.