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A Math Paper of Mine

Here is an interesting math paper that I wrote for a class on Ordinary Differential Equations. The subject is Ergodicity and the Fermi Pasta Ulam system. In 1955, Fermi, Pasta and Ulam wanted to investigate the behavior of nonlinear systems. Nonlinearity had always been suspected of a particular behavior: the dense filling of a configuration space’s energy level surface over a long period of time. Assumptions that followed from that lead to many results in Statistical Mechanics, as well as some paradoxes and problems.

What Fermi found was that oftentimes, nonlinear systems don’t produce anything like ergodic behavior, or equipartition of energy, as was assumed. There may be many unappreciated consequences of this, due to the relative inaccessibility of the behavior of nonlinear systems with many analytical mathematical tools.

Anyway, here it is: