A property of a system that obeys the ergodic hypothesis. The ergodicity of systems has been discussed extensively in the foundations of statistical mechanics, although it is now thought by many physicists to be irrelevant to the problem. Considerations of ergodicity occur in dynamics, since the behaviour can be very complex even for simple dynamical systems (see attractor). Systems, such as spin glasses, in which ergodicity is thought not to hold are described as having broken ergodicity. It is difficult to construct mathematically rigorous proofs of ergodicity in systems. See also KAM theorem.