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An inhomogeneous wave equation and non-linear Diophantine approximation
Research output: Contribution to journal › Article › peer-review
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Publication details
| Journal | Advances in Mathematics |
|---|---|
| Date | Published - 30 Jan 2008 |
| Issue number | 2 |
| Volume | 217 |
| Number of pages | 21 |
| Pages (from-to) | 740-760 |
| Original language | English |
Abstract
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained. (c) 2007 Elsevier Inc. All rights reserved.
- Diophantine approximation, Hausdorff dimension, wave equation, small denominators problem, Diophantine phenomena, HAUSDORFF DIMENSION, SOLVABILITY, VECTORS, FORMS, SETS
Research areas
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Geometrical, dynamical and transference principles in non-linear Diophantine approximation and applications
Project: Research project (funded) › Research
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