Abstract
This paper presents a normal form for the quadratic and cubic terms of a nonlinear discrete time control system around an equilibrium under the group of smooth changes of state coordinates and smooth invertible state feedback. The linear part of the control system need not be controllable. A control bifurcation happens at an equilibrium where there is a loss of linear stabilizability. The paper examines the Neimark-Sacker control bifurcation, and show its relationship to the classical bifurcation of the same name.
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