Abstract
The problem of making a stable discrete time system chaotic has attracted considerable interest. The definition of chaotification used in these studies is based on introducing a feedback control which establishes the existence of a scrambled set for the controlled system. In this note, we introduce a stronger and potentially more useful definition of chaotification based on the existence of an absolutely continuous invariant measure (acim). The utility of this approach is that once a desired chaotic behavior (in the form of an acim near a stable fixed point) is specified, we can determine a small feedback control (as a function of the stable system) such that the controlled dynamical system exhibits the desired behavior. An example is worked out in detail.
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