Sturman, R and Thiffeault, J-L (2019) Lyapunov Exponents for the Random Product of Two Shears. Journal of Nonlinear Science, 29 (2). pp. 593-620. ISSN 0938-8974
Abstract
We give lower and upper bounds on both the Lyapunov exponent and generalised Lyapunov exponents for the random product of positive and negative shear matrices. These types of random products arise in applications such as fluid stirring devices. The bounds, obtained by considering invariant cones in tangent space, give excellent accuracy compared to standard and general bounds, and are increasingly accurate with increasing shear. Bounds on generalised exponents are useful for testing numerical methods, since these exponents are difficult to compute in practice.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Random matrix product; Lyapunov exponent; Generalized Lyapunov exponent |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Sep 2018 14:57 |
Last Modified: | 25 Jun 2023 21:31 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00332-018-9497-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:136194 |
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