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Lyapunov Exponents at Anomalies of SL(2, ℝ)-actions

  • Hermann Schulz-Baldes
Part of the Operator Theory: Advances and Applications book series (OT, volume 174)

Abstract

Anomalies are known to appear in the perturbation theory for the one-dimensional Anderson model. A systematic approach to anomalies at critical points of products of random matrices is developed, classifying and analysing their possible types. The associated invariant measure is calculated formally. For an anomaly of so-called second degree, it is given by the ground-state of a certain Fokker-Planck equation on the unit circle. The Lyapunov exponent is calculated to lowest order in perturbation theory with rigorous control of the error terms.

Keywords

Lyapunov Exponent Invariant Measure Anderson Model Random Dynamical System Dirac Peak 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Hermann Schulz-Baldes
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany

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