There are related mathematical results in symplectic topology and ergodic theory. The ergodic theorem has also had repercussions for dynamics. An ergodic process is one which conforms to the ergodic theorem. These include differential equations, manifolds, Lie groups, and ergodic theory. Stout (1970) generalized the LIL to stationary ergodic martingales. Babylonian thought was also based on an open-systems ontology which is compatible with ergodic axioms. Almost all Bernoulli sequences formula 53 are ergodic sequences. Several kinds of mixing are used in ergodic theory and probability theory. Mathematically, random vibration is characterized as an ergodic and stationary process. Chaos theory began in the field of ergodic theory. The ergodic hypothesis is also important for the Boltzmann approach. The concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory. This is a typical situation in ergodic theory. The study of ergodic systems is part of the larger field of ergodic theory. This is referred to as the "ergodic decomposition" of the measure.