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Undecidability of the word problem and chaos in symbolic dynamics

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Il Nuovo Cimento B (1971-1996)

Summary

The possible existence of deterministic chaos in dynamical systems as connected with Gödelian undecidability of a related formal system rather than to (numerical) untractability of the induced recursion scheme is thoroughly discussed for Markov maps associated with certain subgroups of the modular group (corresponding to flows on manifold with overall negative curvature). The main ingredients are the group-orbit coding of the symbolic dynamics, and the Dehn's word problem for the mapping class group of the manifold. An example is presented and discussed in detail.

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Authors and Affiliations

  1. Dipartimento di Fisica, Politecnico di Torino, 10129, Torino, Italia

    C. Agnes & M. Rasetti

  2. The Institute for Advanced Study, 08540, Princeton, NJ, USA

    M. Rasetti

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  1. C. Agnes
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  2. M. Rasetti
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Agnes, C., Rasetti, M. Undecidability of the word problem and chaos in symbolic dynamics. Nuovo Cim B 106, 879–907 (1991). https://doi.org/10.1007/BF02723184

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