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Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles

Published online by Cambridge University Press:  30 September 2009

S. JITOMIRSKAYA ,
D. A. KOSLOVER  and
M. S. SCHULTEIS
S. JITOMIRSKAYA
Affiliation:
Department of mathematics, University of California, Irvine, CA 92697, USA (email: szhitomi@math.uci.edu)
D. A. KOSLOVER
Affiliation:
Department of mathematics, University of California, Irvine, CA 92697, USA (email: szhitomi@math.uci.edu) Department of mathematics, University of Texas at Tyler, Tyler, TX 75799, USA (email: dkoslover@uttyler.edu)
M. S. SCHULTEIS
Affiliation:
Department of mathematics, University of California, Irvine, CA 92697, USA (email: szhitomi@math.uci.edu) Department of mathematics, Concordia University, Irvine, CA 92612, USA (email: melinda.schulteis@cui.edu)
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Abstract

It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasiperiodic cocycles. In this paper we show that it is continuous in the analytic category. Our corollaries include continuity of the Lyapunov exponent associated with general quasiperiodic Jacobi matrices or orthogonal polynomials on the unit circle, in various parameters, and applications to the study of quantum dynamics.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 6 , December 2009 , pp. 1881 - 1905
Copyright
Copyright © Cambridge University Press 2009

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