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

In: Handbook of the Mathematics of the Arts and Sciences

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  • Doğan Çömez

    (North Dakota State University, Department of Mathematics)

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.

Suggested Citation

  • Doğan Çömez, 2021. "Modern Ergodic Theory: From a Physics Hypothesis to a Mathematical Theory with Transformative Interdisciplinary Impact," Springer Books, in: Bharath Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, chapter 76, pages 1969-1992, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-57072-3_31
    DOI: 10.1007/978-3-319-57072-3_31
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