Modern Ergodic Theory: From a Physics Hypothesis to a Mathematical Theory with Transformative Interdisciplinary Impact

Doğan Çömez ()
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Doğan Çömez: North Dakota State University, Department of Mathematics

Chapter 76 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 1969-1992 from Springer

Abstract: Abstract Ergodic theory emerged as a statistical mechanics hypothesis and has quickly reached into a mature and influential mathematical theory. Beginning with a brief historical account on the origins of the theory, the first two sections of this chapter aim to provide a broad exposé of some major results in ergodic theory and dynamical systems. The remaining sections are devoted to the discussion of the interdisciplinary nature of ergodic theory from a broad perspective. Select applications of the theory are outlined, and its interactions with other mathematical fields and with some nonmathematical disciplines are briefly illustrated.

Keywords: Ergodic theory; Dynamical system; Ergodic transformation; Measure-preserving transformation; Invariant measure; Interdisciplinary aspects of ergodic theory (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57072-3_31

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DOI: 10.1007/978-3-319-57072-3_31

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