Kinematics of complex movement

We present a deterministic discrete dynamical system which is used to classify and simulate complex irregular motion, in two or three dimension. The dynamical system is defined by a two-parameter family of bimodal interval maps which give directly the displacements through iteration. A trajectory is composed of patches of linear motions, through the plane, intertwined by changes of direction. The characterization of the movements is obtained from the topological classification of the interval map family. The used techniques arise from symbolic dynamics and topological Markov chains, developed by Sousa Ramos and his collaborators. The main classifying tool is the kneading invariant which consist on the symbolic itinerary of the critical points of the interval maps. We produce a catalogue or dictionary of typical trajectories and for each kneading invariant we explicit certain features, such as topological entropy, average area covered, length distribution probability, among others.