Abstract
We discuss controllability properties of non-invertible nonlinear discretetime systems under the assumption of forward accessibility. It is shown how regularity properties of control sequences can be used in the construction of regions of complete controllability, i.e. control sets. Some properties of control sets are discussed, and the existence of regular controls with periodic points in a prescribed region of a control set is shown. Furthermore, the parameter dependence of control sets and chain control sets is analyzed.
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