The existence of a bounded trajectory is decidable
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چکیده
In the following, M,M denote respectively the set of all products of matrices in M, and the set of all products of length t of matrices in M. This problem is closely related to the so called joint spectral subradius of a set of matrices, which is the smallest asymptotic rate of growth of any long product of matrices in the set, when the length of the product increases. For a survey on the joint spectral subradius and similar quantities, see [2]. While the joint spectral subradius is notoriously Turing-uncomputable in general, we will see that in our precise situation, we are able to provide an algorithmic solution to the problem. We first show that one should not expect a polynomial time algorithm for the problem.
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