Abstract
Here we introduce the concept of measure-preserving transformations and then define and illustrate three levels of irregular behavior that such transformations can display. These three levels are known as ergodicity, mixing, and exactness. The central theme of the chapter is to show the utility of the Frobenius–Perron and Koopman operators in the study of these behaviors.
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© 1994 Springer Science+Business Media New York
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Lasota, A., Mackey, M.C. (1994). Studying Chaos with Densities. In: Chaos, Fractals, and Noise. Applied Mathematical Sciences, vol 97. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4286-4_4
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DOI: https://doi.org/10.1007/978-1-4612-4286-4_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8723-0
Online ISBN: 978-1-4612-4286-4
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