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:
“... it is as true in morals as in physics that all force is imperishable; therefore the consequences of a human action never cease.”
—Tennessee Claflin (1846–1923)
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)
“Won’t this whole instinct matter bear revision?
Won’t almost any theory bear revision?
To err is human, not to, animal.”
—Robert Frost (1874–1963)