Discrete symmetries of chaotic strings

Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. In this article we look at two important properties of chaotic strings, namely (i) the behaviour under discrete symmetry transformations and (ii) the loss of ergodic behaviour in certain coupling regions. We show that several of the chaotic string dynamics can be transformed into each other by simple discrete coordinate transformations. We investigate how expectation values converge in the various coupling parameter regions and single out those stable zeros of the correlation function that correspond to ergodic states with well-defined convergence properties.