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

Schulz-Baldes H (2007)


Publication Type: Book chapter / Article in edited volumes

Publication year: 2007

Publisher: Birkhäuser

Edited Volumes: Operator Theory, Analysis and Mathematical Physics

Series: Operator Theory: Advances and Applications

City/Town: Basel

Book Volume: 174

Pages Range: 159-172

ISBN: 978-3-7643-8134-9

URI: http://de.arxiv.org/abs/math-ph/0607026

DOI: 10.1007/978-3-7643-8135-6_10

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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How to cite

APA:

Schulz-Baldes, H. (2007). Lyapunov Exponents at Anomalies of SL(2, ℝ)-actions. In Jan Janas, Pavel Kurasov, Ari Laptev, Sergei Naboko, Günter Stolz (Eds.), Operator Theory, Analysis and Mathematical Physics. (pp. 159-172). Basel: Birkhäuser.

MLA:

Schulz-Baldes, Hermann. "Lyapunov Exponents at Anomalies of SL(2, ℝ)-actions." Operator Theory, Analysis and Mathematical Physics. Ed. Jan Janas, Pavel Kurasov, Ari Laptev, Sergei Naboko, Günter Stolz, Basel: Birkhäuser, 2007. 159-172.

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