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This subtopic studies measure-theoretic ergodic theory, connecting invariant measures, recurrence, and long-term dynamical behavior.
28D05 studies measure-preserving transformations in measure-theoretic ergodic theory. It studies dynamical systems from a measure-theoretic viewpoint, focusing on invariant measures and long-term statistical behavior.
Measure-Theoretic Ergodic Theory (Wikipedia)
Used to prove recurrence, mixing, and convergence results in dynamics.
28D10 studies one-parameter continuous families of measure-preserving transformations in measure-theoretic ergodic theory. It studies dynamical systems from a measure-theoretic viewpoint, focusing on invariant measures and long-term statistical behavior.
Measure-Theoretic Ergodic Theory (Wikipedia)
Used to prove recurrence, mixing, and convergence results in dynamics.
28D15 studies general groups of measure-preserving transformations in measure-theoretic ergodic theory. It studies dynamical systems from a measure-theoretic viewpoint, focusing on invariant measures and long-term statistical behavior.
Measure-Theoretic Ergodic Theory (Wikipedia)
Used to prove recurrence, mixing, and convergence results in dynamics.
28D20 studies entropy and other invariants in measure-theoretic ergodic theory. It studies dynamical systems from a measure-theoretic viewpoint, focusing on invariant measures and long-term statistical behavior.
Measure-Theoretic Ergodic Theory (Wikipedia)
Used to prove recurrence, mixing, and convergence results in dynamics.