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- W2561738181 abstract "We prove that the non-linear quasi-periodically forced harmonic oscillator with two frequencies <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis 1 comma alpha right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>α<!-- α --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(1,alpha )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has at least one response solution if the forcing is small. No arithmetic condition on the frequency is assumed and the smallness of the non-linear forcing does not depend on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=alpha> <mml:semantics> <mml:mi>α<!-- α --></mml:mi> <mml:annotation encoding=application/x-tex>alpha</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The result strengthens the existing results in the literature where the frequency is assumed to be Diophantine. The proof is based on a modified KAM theory for the lower dimensional tori." @default.
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- W2561738181 date "2016-12-22" @default.
- W2561738181 modified "2023-10-14" @default.
- W2561738181 title "Response solutions for quasi-periodically forced harmonic oscillators" @default.
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- W2561738181 doi "https://doi.org/10.1090/tran/6800" @default.
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