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About this paper
Jordan Cotler, Semon Rezchikov
A framework defines how smooth, finite-dimensional continuous dynamical systems can robustly simulate discrete computation, establishing computational limits for various system types. The work constructs a smooth 2-disk diffeomorphism that is robustly Turing-universal and proves that both Axiom A and measure-preserving systems are not universally computable under this robust definition.
Key insights
- A rigorous definition of continuous computation must account for the computational complexity of encoders and decoders to prevent the 'computational triviality problem'.
- Robust universal computation requires specific dynamical properties; neither uniformly chaotic (Axiom A) nor perfectly ordered (measure-preserving/integrable) systems can achieve it.
- The work lays the groundwork for a new research program to systematically classify dynamical systems based on their intrinsic computational power, bridging complexity theory with dynamical systems theory.
Summary by alphaXiv.
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