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The Hausdorff Dimension of Exceptional Sets Associated with Normal Forms |
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| Authors: | Dodson M M; Rynne B P; Vickers J A G |
| Institution: | Department of Mathematics, University of York York YOl 5DD Department of Mathematics, Heriot-Watt University Edinburgh EH1 1HX Department of Mathematics, University of Southampton Southampton SO9 5NH |
| Abstract: | The Hausdorff dimension is obtained for exceptional sets associatedwith linearising a complex analytic diffeomorphism near a fixedpoint, and for related exceptional sets associated with obtaininga normal form of an analytic vector field near a singular point.The exceptional sets consist of eigenvalues which do not satisfya certain Diophantine condition and are ‘close’to resonance. They are related to ‘lim-sup’ setsof a general type arising in the theory of metric Diophantineapproximation and for which a lower bound for the Hausdorffdimension has been obtained. |
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