Exact Lyapunov Exponent for Infinite Products of Random Matrices

Details Exact Lyapunov Exponent for Infinite Products of Random Matrices Exact Lyapunov Exponent for Infinite Products of Random Matrices

1994-07-26

arxiv.org/abs/chao-dyn/9407013v1

Nonlinear Sciences

Chaotic Dynamics

1 pages, CPT-93/P.2974,latex

Scientific paper

10.1088/0305-4470/27/10/019

In this work, we give a rigorous explicit formula for the Lyapunov exponent for some binary infinite products of random $2\times 2$ real matrices. All these products are constructed using only two types of matrices, $A$ and $B$, which are chosen according to a stochastic process. The matrix $A$ is singular, namely its determinant is zero. This formula is derived by using a particular decomposition for the matrix $B$, which allows us to write the Lyapunov exponent as a sum of convergent series. Finally, we show with an example that the Lyapunov exponent is a discontinuous function of the given parameter.

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