Poincaréåterkomst
Poincaré återkomst, commonly known in English as the Poincaré recurrence theorem, is a result in dynamical systems and ergodic theory named after Jules Henri Poincaré, who proved it in 1890. The theorem concerns the behavior of measure-preserving dynamical systems with finite total measure. Roughly speaking, it states that any region of the state space with positive measure will be revisited by the system's trajectory arbitrarily many times.
Formal statement: Let (X, Σ, μ) be a measure space with μ(X) < ∞ and T: X → X a measurable
The theorem holds for discrete-time systems and has analogues for continuous-time flows. It implies recurrence: in
Consequences and context: Poincaré recurrence is a foundational result in ergodic theory and underpins arguments about