Abstract
Consider a dynamical system, modeled by the data of a phase space X, a transformation T: X → X describing the evolution of the system over time, and a finite measure μ representing an extensive quantity conserved during the motion. We wish to study the sequence {T n(x)} n ∈ N , which represents the succession of states the system takes on over time. This sequence makes up the trajectory of the point x, or its orbit.
Le second, de diviser chacune des difficultés que j’examinerois, en autant de parcelles qu’il se pourroit, et qu’il seroit requis pour les mieux résoudre.
R. Descartes (1596–1650)
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References
Krengel, U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter & Co., Berlin (1985)
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Coudène, Y. (2016). The Pointwise Ergodic Theorem. In: Ergodic Theory and Dynamical Systems. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-7287-1_2
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DOI: https://doi.org/10.1007/978-1-4471-7287-1_2
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