  We introduce combinatorial multivector fields, associate with them
multivalued dynamics and study their topological features. Our combinatorial
multivector fields generalize combinatorial vector fields of Forman. We define
isolated invariant sets, Conley index, attractors, repellers and Morse
decompositions. We provide a topological characterization of attractors and
repellers and prove Morse inequalities. The generalization aims at algorithmic
analysis of dynamical systems through combinatorialization of flows given by
differential equations and through sampling dynamics in physical and numerical
experiments. We provide a prototype algorithm for such applications.
