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Lyapunov exponent and rotation number for stochastic Dirac operators (1992)

Sun, Fengzhu ; Qian, Minping

Springer

Acta mathematicae applicatae sinica 8 (1992), S. 333-347

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ISSN: 1618-3932

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02006742

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