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A fundamental result in dynamical systems that provides conditions under which the time average of a function along the orbits of the system is equal to the space average over the whole phase space.

A function that represents the relationship between successive intersections of a trajectory of a dynamical system with the Poincaré section.

A system in which a function describes the time dependence of a point in a geometrical space. Used to model the evolution of a system over time.

Used to analyze the stability of periodic solutions in a dynamical system, particularly by studying the eigenvalues of the monodromy matrix, also known as the Floquet multipliers.

A specific type of recurrence plot that helps to find the periodic orbits of a continuous dynamical system by intersecting its trajectory with a lower-dimensional subspace, called the Poincaré section.

A point in the phase space of a dynamical system that is invariant under the system dynamics, meaning that if the system starts at this point, it will remain there forever.

An orbit of a dynamical system that repeats itself after some finite time period T, forming a closed trajectory in phase space.

A trajectory of a dynamical system that leaves a saddle fixed point and then returns to the same fixed point as time goes to infinity.

A measure of the rate of separation of infinitesimally close trajectories in a dynamical system, indicating the presence and strength of chaos.

In a dynamical system, these manifolds consist of all points that asymptotically approach or recede from a fixed point, respectively, as time goes to infinity.

A measure that remains unchanged by the evolution of the dynamical system, often used in the context of ergodic theory and the statistical properties of dynamic systems.