Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Ergodic Theory: Rigidity

  • Viorel Niţică
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_185

Definition of the Subject

As one can see from this volume, chaotic behavior of complex dynamical systems is prevalent in nature and in large classes oftransformations. Rigidity theory can be viewed as the counterpart to the generic theory of dynamical systems which often investigates chaotic dynamics fora typical transformation belonging to a large class. In rigidity one is interested in finding obstructions to chaotic, or generic,behavior. This often leads to rather unexpected classification results. As such, rigidity in dynamics and ergodic theory is difficult to define preciselyand the best approach to this subject is to study various results and themes that developed so far. A classification is offered below in local,global, differentiable and measurable rigidity. One should note that all branches are strongly intertwined and, at this stage of the development of thesubject, it is difficult to separate them.

Rigidity is a well developed and prominent topic in modern mathematics....

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Notes

Acknowledgment

This research was supported in part by NSF Grant DMS-0500832.

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Authors and Affiliations

  • Viorel Niţică
    • 1
    • 2
  1. 1.West Chester UniversityWest ChesterUSA
  2. 2.Institute of MathematicsBucharestRomania