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IMPROVING AN INEQUALITY FOR THE DIVISOR FUNCTION
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 3 / June 2018
- Published online by Cambridge University Press:
- 28 March 2018, pp. 374-381
- Print publication:
- June 2018
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- Article
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ANALYTIC REDUCIBILITY OF RESONANT COCYCLES TO A NORMAL FORM
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 15 / Issue 1 / January 2016
- Published online by Cambridge University Press:
- 27 November 2014, pp. 203-223
- Print publication:
- January 2016
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- Article
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We consider systems of quasi-periodic linear differential equations associated to a ‘resonant’ frequency vector
${\it\omega}$, namely, a vector whose coordinates are not linearly independent over 
$\mathbb{Z}$. We give sufficient conditions that ensure that a small analytic perturbation of a constant system is analytically conjugate to a ‘resonant cocycle’. We also apply our results to the non-resonant case: we obtain sufficient conditions for reducibility.
