George David Birkhoff is most famous for his work on transformations with this property.
It's not chaos, but Eberhard Hopf proved this property for geodesic flows on manifolds with negative curvature, which generalized dynamical billiards named for Jacques Hadamard and Emil Artin. Hermann Weyl proved a strong form of this property for the fractional parts of the integer multiples of a given irrational number. George David Birkhoff is most famous for his work on transformations with this property. A measure-preserving transformation has the abstract form of property, if every set that it fixes has either measure zero or measure one. A prize problem to determine the long-term stability of the solar system motivated (*) Poincaré to show that an infinitely-repeated measure-preserving transformation gives a property slightly weaker than this one, in his recurrence theorem. Equidistribution is a strong form of this property, which is assumed in the proof of the equipartition theorem. For 10 points, name this property of a system in which, over time, all accessible states are equally likely, and which names a fundamental hypothesis in thermodynamics.
It's not chaos, but Eberhard Hopf proved this property for geodesic flows on manifolds with negative curvature, which generalized dynamical billiards named for Jacques Hadamard and Emil Artin.
ergodicity [accept word forms like ergodic; accept ergodic things like the ergodic hypothesis; anti- prompt on "equidistributed" or word forms] 