Abstract
In this paper, by the KAM method, under weaker small denominator conditions and nondegeneracy conditions, we prove a positive measure reducibility for quasi-periodic linear systems close to constant: Ẋ = (A(λ) + F(ϕ, λ))X, \( \dot{\varphi } = \omega \)where the parameter λ ∈ (a, b), ω is a fixed Diophantine vector, which is a generalization of Jorba & Simó’s positive measure reducibility result.
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The work is supported by the National Natural Science Foundation of China (19925107) and the Special Funds for Major State Basic Research Projects (973 Projects)
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He, H.L., You, J.G. An Improved Result for Positive Measure Reducibility of Quasi-periodic Linear Systems. Acta Math Sinica 22, 77–86 (2006). https://doi.org/10.1007/s10114-004-0473-5
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DOI: https://doi.org/10.1007/s10114-004-0473-5