Abstract
Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time average exists and is equal to the space average. The applications of ergodic theory are the main concern of this note. We will introduce fundamental concepts in ergodic theory, Birkhoff’s ergodic theorem and its consequences.
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References
R. Durrett, Probability: Theory and Examples, 4th edn. (Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010)
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Trinh, K.D. (2014). An Introduction to Ergodic Theory. In: Nishii, R., et al. A Mathematical Approach to Research Problems of Science and Technology. Mathematics for Industry, vol 5. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55060-0_22
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DOI: https://doi.org/10.1007/978-4-431-55060-0_22
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