An algebraic approach to discrete mechanics (Q1330305)

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