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Lyapunov exponent and rotation number for stochastic Dirac operators

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Abstract

In this paper, we consider the stochastic Dirac operator

$$L_\omega = \left( {\begin{array}{*{20}c} 0{ - 1} \\ 10 \\ \end{array} } \right)\frac{d}{{dt}} - \left( {\begin{array}{*{20}c} {p(T_t \omega )}0 \\ { 0}{q(T_t \omega )} \\ \end{array} } \right)$$

on a polish space (Θ, β,P). The relation between the Lyapunov index, rotation number and the spectrum ofL ω is discussed. The existence of the Lyapunov index and rotation number is shown. By using the W-T functions and W-function we prove the theorems forL ω as in Kotani [1], [2] for Schrödinger operators, and in Johnson [5] for Dirac operators on compact space.

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Authors and Affiliations

  1. Shandong University, 250100, Jinan, China

    Sun Fengzhu

  2. Peking University, 100871, Beijing, China

    Qian Minping

Authors
  1. Sun Fengzhu
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  2. Qian Minping
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Sun, F., Qian, M. Lyapunov exponent and rotation number for stochastic Dirac operators. Acta Mathematicae Applicatae Sinica 8, 333–347 (1992). https://doi.org/10.1007/BF02006742

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  • DOI: https://doi.org/10.1007/BF02006742

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