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

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Handbook of the Mathematics of the Arts and Sciences

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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.

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Authors and Affiliations

  1. Department of Mathematics, North Dakota State University, Fargo, ND, USA

    Doğan Çömez

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  1. Doğan Çömez
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Correspondence to Doğan Çömez .

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Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Torsten Lindström

  2. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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Çömez, D. (2019). Modern Ergodic Theory: From a Physics Hypothesis to a Mathematical Theory with Transformative Interdisciplinary Impact. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_31-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_31-1

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