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Communications in Mathematical Physics

, Volume 28, Issue 3, pp 237–243 | Cite as

Perturbations of the modular automorphism group

  • Richard H. Herman
Article

Abstract

It is shown, under a necessary condition, that strong (pointwise) convergence of modular automorphism groups to a one parameter family of maps implies weak convergence of the respective states in the factor case. Moreover the limiting one parameter family of maps is the modular automorphism group for the limiting state. In the type I case weak convergence of the automorphism groups suffices. Norm convergence of the states is obtained in some cases.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Automorphism Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Richard H. Herman
    • 1
    • 2
  1. 1.University of CaliforniaLos Angeles
  2. 2.Pennsylvania State UniversityState College

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