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Micro-chaos in digital control. (English) Zbl 0863.93050
The authors study the ‘micro chaos’ map \(F:x \to ax - b\text{Int} (x)\), describing the local dynamics of a digitally controlled unstable system, being subject to a linear effect of sampling and a nonlinear effect of round-off. These effects frequently cause chaotic oscillations on a microscopic scale near the equilibrium. The authors prove the existence of a hyperbolic strange attractor for a large set of parameter values of the map \(F\) and study its domain of attraction – being of full measure but possibly having a fractal boundary. Finally, they describe the dynamics on the fractal attractor using symbolic dynamics.

MSC:
93C62 Digital control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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