The concept of discrete multivalued dynamical systems for noncommutative CW complexes is developed. Stable and unstable manifolds are introduced and their role in geometric and topological configurations of noncommutative CW complexes is studied. Our technique is illustrated by an example on the noncommutative CW complex decomposition of the algebra of continuous functions on two dimensional torus.2010 MSC: 46L85, 55U10, 54H20, 34D35.

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a b s t r a c tWe propose a new approach, based on the Conley index theory, for the detection and classification of critical regions in multidimensional data sets. The use of homology groups makes this method consistent and successful in all dimensions and allows us to generalize visual classification techniques based solely on the notion of connectedness which may fail in higher dimensions.