Devaney chaos

Summary

Devaney chaos is a precise definition of a chaotic map, proposed by Robert Devaney in his textbook on chaotic dynamical systems. A continuous map of a metric space is chaotic in this sense when three things hold. It is topologically transitive, its periodic points are dense, and it has sensitive dependence on initial conditions. It turns the informal ideas of chaos theory into conditions that can be checked. For infinite spaces the third condition follows from the first two.