ANTI-CONTROL OF DISCRETE CHAOS IN BANACH SPACES

This paper is concerned with anti-control (or, chaotification) of chaos for discrete dynamical systems in general and some special Banach spaces, via feedback control techniques. The controlled systems are proved to be chaotic in the sense of both Devaney and Li-Yorke. The original system can be driven to be chaotic by using an arbitrarily small-amplitude state feedback control in certain Banach spaces. In addition, the Chen-Lai anti-control algorithm via feedback control with mod-operation in a finite-dimensional real space is extended to a certain infinite-dimensional Banach space, and the controlled system is shown chaotic in the sense of Devaney as well as in the sense of both Li-Yorke and Wiggins in both finite-dimensional and infinitedimensional spaces. Key words anti-control of chaos, discrete dynamical system, Banach