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Effective estimates on the top Lyapunov exponents for random matrix products

Jurga, Natalia and Morris, Ian (2019) Effective estimates on the top Lyapunov exponents for random matrix products Nonlinearity.

Effective estimates on the top lyapunov exponents for random matrix products.pdf - Accepted version Manuscript

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We study the top Lyapunov exponents of random products of positive 2×2 matrices and obtain an efficient algorithm for its computation. As in the earlier work of Pollicott, the algorithm is based on the Fredholm theory of determinants of trace-class linear operators. In this article we obtain a simpler expression for the approximations which only require calculation of the eigenvalues of finite matrix products and not the eigenvectors. Moreover, we obtain effective bounds on the error term in terms of two explicit constants: a constant which describes how far the set of matrices are from all being column stochastic, and a constant which measures the minimal amount of projective contraction of the positive quadrant under the action of the matrices.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 2019
Funders : Leverhulme Trust
Copyright Disclaimer : © 2019 IOP Publishing Ltd & London Mathematical Society
Related URLs :
Depositing User : Clive Harris
Date Deposited : 18 Sep 2019 13:51
Last Modified : 18 Sep 2019 13:52

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