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
Famous quotes containing the words physics, systems and/or theory:
“He who is conversant with the supernal powers will not worship these inferior deities of the wind, waves, tide, and sunshine. But we would not disparage the importance of such calculations as we have described. They are truths in physics because they are true in ethics.”
—Henry David Thoreau (1817–1862)
“The skylines lit up at dead of night, the air- conditioning systems cooling empty hotels in the desert and artificial light in the middle of the day all have something both demented and admirable about them. The mindless luxury of a rich civilization, and yet of a civilization perhaps as scared to see the lights go out as was the hunter in his primitive night.”
—Jean Baudrillard (b. 1929)
“The great tragedy of science—the slaying of a beautiful theory by an ugly fact.”
—Thomas Henry Huxley (1825–1895)