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Non-Turing Universality for Certain Non-Uniformly Hyperbolc Computational Dynamical Systems
Lane, Darby
Lane, Darby
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Abstract
In the interest of designing a framework allowing simulation of computation by a dynamical system, the
authors of [CR24] defined and proved preliminary results for a Computational Dynamical System, enabling
the rigorous study of the computational capacity of a dynamical system. Among their results is the conclusion
that neither highly chaotic systems such as Axiom A systems, nor highly regular systems, such as compact,
measure-preserving systems or integrable systems, can robustly simulate a universal Turing machine. In this
thesis we extend these results by proving that non-uniform hyperbolicity, which allows for a combination of
regular and chaotic behavior within a dynamical system, does not guarantee robust simulation of a universal
Turing machine.
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2026-04-30
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Mathematics and Statistics