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Analysis of positive measure reducibility for quasi-periodic linear systems under Brjuno-Russmann condition
Journal article   Open access  Peer reviewed

Analysis of positive measure reducibility for quasi-periodic linear systems under Brjuno-Russmann condition

Muhammad Afzal, Tariq Ismaeel, Riaz Ahmad, Ilyas Khan, Dumitru Baleanu and Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
AIMS mathematics, Vol.7(5), pp.9373-9388
01/01/2022
DOI: https://doi.org/10.3934/math.2022520

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In this article, we discuss the positive measure reducibility for quasi-periodic linear systems close to a constant which is defined as: dx/dt = (A(lambda) + Q(phi, lambda))x, (phi) over dot = omega, where omega is a Brjuno vector and parameter lambda is an element of (a, b). The result is proved by using the KAM method, Brjuno-Russmann condition, and non-degeneracy condition.
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https://doi.org/10.3934/math.2022520View
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