A measure that is invariant under all measure-preserving transformations.

A measure that is concentrated on a single point.

A measure that is absolutely continuous with respect to Lebesgue measure.

A measure that is singular with respect to Lebesgue measure.

A theorem that states that the time average of a function along a trajectory of a dynamical system is equal to the spatial average of the function.

A theorem that states that the measure-preserving transformations of a dynamical system are ergodic.

A theorem that states that the entropy of a dynamical system is equal to the logarithm of the number of ergodic measures.

A theorem that states that the Lyapunov exponents of a dynamical system are equal to the eigenvalues of the transfer operator.

An operator that acts on functions on the phase space of a dynamical system.

An operator that acts on measures on the phase space of a dynamical system.

An operator that acts on transformations of the phase space of a dynamical system.

An operator that acts on the entropy of a dynamical system.

A measure of the randomness of a dynamical system.

A measure of the complexity of a dynamical system.

A measure of the predictability of a dynamical system.

A measure of the stability of a dynamical system.

A measure of the rate of divergence of nearby trajectories in a dynamical system.

A measure of the rate of convergence of nearby trajectories in a dynamical system.

A measure of the stability of a dynamical system.

A measure of the predictability of a dynamical system.