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I've been able to find a decent amount of existing resources for computing the Lyapunov Exponents for a system of differential equations. Is there any existing code/resources for computing the Covariant Lyapunov Vectors?

Cheyne
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  • Have e.g. a look at:" https://mathematica.stackexchange.com/questions/17593/lyapunov-exponent" and "http://www.msandri.it/soft.html" or: "https://venturi.soe.ucsc.edu/sites/default/files/Numerical_Calculation_of_Lyapunov_Exponents.pdf" – Daniel Huber Oct 16 '20 at 11:43
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    @DanielHuber I suppose those links are about Lyapunov Exponents, not Lyapunov Vectors. Cheyne, I haven't heard of these but it sounds interesting. Can you provide some links to more info, including an algorithm if one exists, and what they are used for? – Chris K Oct 16 '20 at 14:46
  • Gladly, here are some sources: – Cheyne Oct 16 '20 at 16:36
  • These sources gives some general mathematical explanation:
    https://link.springer.com/article/10.1007/s00332-012-9126-5
    https://iopscience.iop.org/article/10.1088/1751-8113/46/25/254005     – Cheyne Oct 16 '20 at 16:37
  • This source gives some small excerpts of matlab code and compares algorithms:
    https://www.sciencedirect.com/science/article/abs/pii/S0167278912003090     – Cheyne Oct 16 '20 at 16:38
  • The Covariant Lyapunov Vectors coincide with the Floquet eigenvectors when computed along periodic orbits if that gives you some sense. This paper discusses some uses of the vectors: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.99.130601 – Cheyne Oct 16 '20 at 16:39
  • @ChrisK Does your EcoEvo package find floquet vectors for generic limit cycles? – Cheyne Oct 16 '20 at 17:18
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    @Cheyne Only Floquet exponents/multipliers .. I haven't had an opportunity to think about the corresponding vectors, but it is intriguing, so thanks for the links – Chris K Oct 16 '20 at 18:43
  • I may be minunderstanding, but are the EcoEigenvalues (floquet multipliers) the eigenvalues of the EcoJacobian (which would then be the Monodromy Matrix in Floquet Theory), therefore the Floquet vectors I'm looking for would be the eigenvectors of the EcoJacobian? – Cheyne Oct 16 '20 at 22:26

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