Topological mixing

Topological mixing is a property of dynamical systems that ensures any open region of phase space will eventually overlap with any other open region under the system's evolution. Unlike mere ergodicity, which requires only that the system visits every region with correct frequency, mixing demands that the system thoroughly interweaves distinct regions until they become statistically indistinguishable. It is the mathematical formalization of the intuition that a chaotic system "stirs" its state space rather than merely wandering through it.

Topological mixing is one of the three defining properties of deterministic chaos in the Devaney definition, alongside sensitive dependence on initial conditions and dense periodic orbits. Without mixing, a system might be sensitive and unpredictable yet still confine trajectories to separate, non-interacting regions. Mixing guarantees that information — and ignorance — spreads globally. The rate at which mixing occurs is measured by the mixing time, which quantifies how quickly correlations decay and the system forgets its initial configuration.