On the neighborhood in stabilizing period-T orbits for chaotic m degree polynomial dynamical system

In this paper, a problem of stabilizing a period-T orbit in discrete chaotic m degree polynomial dynamical systems is studied. The aim is to present a new method for determining the neighborhood of a period-T point in which the system remains stable when subjected to a linear feedback control. A theorem on the existence of neighborhood is rigorously proved using idea from functional analysis and polar coordinate transformation. The ways of implementing the obtained theorem in the Hénon map are proposed. The validity of this method is shown by numerical simulation.