AN ALGEBRAIC APPROACH TO DISCRETE MECHANICS

Using basic ideas from algebraic geometry, we extend the methods of La grangian and symplectic mechanics to treat a large class of discrete m echanical systems, that is, systems such as cellular automata in which time proceeds in integer steps and the configuration space is discret e. In particular, we derive an analog of the Euler-Lagrange equation f rom a variational principle, and prove an analog of Noether's theorem. We also construct a symplectic structure on the analog of the phase s pace, and prove that it is preserved by time evolution.