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

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Operator Theory, Analysis and Mathematical Physics

Part of the book series: Operator Theory: Advances and Applications ((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.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarkstr. 1 1/2, D-91054, Erlangen, Germany

    Hermann Schulz-Baldes

Authors
  1. Hermann Schulz-Baldes
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Editor information

Editors and Affiliations

  1. Institut of Mathematics, Polish Academy of Sciences, ul. Sw. Tomasza 30/7, 31-027, Krakow, Poland

    Jan Janas

  2. Department of Mathematics, Lund Institute of Technology, 221 00, Lund, Sweden

    Pavel Kurasov

  3. Dept. of Mathematics, Imperial College London, Room 675 South Kensington Campus, SW7 2AZ, London, UK

    Ari Laptev

  4. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Ari Laptev

  5. Department of Mathematical Physics, St. Petersburg State University, Ulyanovskaya 1, 198904, St. Petersburg, Russia

    Sergei Naboko

  6. Department of Mathematics, University of Alabama, 452 Campbell Hall, Birmingham, AL, 35294-1170, USA

    Günter Stolz

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Schulz-Baldes, H. (2007). Lyapunov Exponents at Anomalies of SL(2, ℝ)-actions. In: Janas, J., Kurasov, P., Laptev, A., Naboko, S., Stolz, G. (eds) Operator Theory, Analysis and Mathematical Physics. Operator Theory: Advances and Applications, vol 174. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8135-6_10

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