Some aspects of dynamical systems.

Flows which are suspensions of auto-diffeomorphisms of manifolds are studied in this thesis. The structure of the product of two such suspended flows is investigated and its relation to product diffeomorphisms, together with some simple statements concerning Anosov flows are given. A generalization of suspension to deal with any finite number of commuting auto-diffeomorphisms is considered and analogous results to those obtained above are proved together with some additional ones. A functorial representation is given for suspended flows. Other flow invariant operations on manifolds are considered for this class of flows. Also considered are diffeomorphisms with non-wandering sets which have parts homeomorphic to Cantor Sets. The cohomologies of their insets are computed using Cech cohomology theory. This is a first step in the problem of using Morse Theory to obtain Morse-inequalities for Smale diffeomorphisms as defined in the introduction.