Discrete dynamics on noncommutative CW complexes

Abstract

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.

Keywords

• closed hemi-continuous, C*-algebra, CW complexes, discrete dynamical system, modified Morse function, noncommutative CW complex, open hemi-continuous, stable manifold, unstable manifold