Physics and Dynamical Systems Theory
Omohundro's book Geometric Perturbation Theory in Physics describes natural Hamiltonian symplectic structures for a wide range of physical models that arise from perturbation theory analyses.
He showed that there exist smooth partial differential equations which stably perform universal computation by simulating arbitrary cellular automata. The asymptotic behavior of these PDEs is therefore logically undecidable.
With John David Crawford he showed that the orbits of three-dimensional period doubling systems can form an infinite number of topologically distinct torus knots and described the structure of their stable and unstable manifolds.
Read more about this topic: Steve Omohundro
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