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

  • Doğan ÇömezEmail author
Living reference work entry

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 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsNorth Dakota State UniversityFargoUSA

Section editors and affiliations

  • Torsten Lindström
    • 1
  • Bharath Sriraman
    • 2
  1. 1.Department of MathematicsLinnaeus UniversityVäxjöSweden
  2. 2.Department of Mathematical SciencesThe University of MontanaMissoulaUSA

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