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Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs


Author: Janusz Mierczyński
Journal: Proc. Amer. Math. Soc. 143 (2015), 1127-1135
MSC (2010): Primary 34C12, 34D08, 37C65; Secondary 15B48, 92D25
DOI: https://doi.org/10.1090/S0002-9939-2014-12368-9
Published electronically: November 24, 2014
MathSciNet review: 3293728
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Abstract: For cooperative random linear systems of ordinary differential equations a method is presented of obtaining lower estimates of the top Lyapunov exponent. The proofs are based on applying some polynomial Lyapunov-like function. Known estimates for the dominant eigenvalue of a nonnegative matrix due to G. Frobenius and L. Yu. Kolotilina are shown to be specializations of our results.


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Additional Information

Janusz Mierczyński
Affiliation: Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, PL-50-370 Wrocław, Poland
Email: mierczyn@pwr.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-2014-12368-9
Received by editor(s): May 25, 2013
Published electronically: November 24, 2014
Additional Notes: The author was supported by project S20058/I-18.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2014 American Mathematical Society