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Deciding stability and mortality of piecewise affine dynamical systems. (English) Zbl 0973.68067
Summary: In this paper we study problems such as: given a discrete time dynamical system of the form $$x(t+1)=f (x(t))$$ where $$f: R^{n}\rightarrow R^{n}$$ is a piecewise affine function, decide whether all trajectories converge to 0. We show in our main theorem that this attractivity problem is undecidable as soon as $$n\geqslant 2$$. The same is true of two related problems: Stability (is the dynamical system globally asymptotically stable?) and mortality (do all trajectories go through 0?). We then show that attractivity and stability become decidable in dimension 1 for continuous functions.

##### MSC:
 68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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##### References:
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