The Hausdorff Dimension of Exceptional Sets Associated with Normal Forms | Zendy

Dodson M. M. | Zendy; Rynne B. P. | Zendy; Vickers J. A. G. | Zendy

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The Hausdorff Dimension of Exceptional Sets Associated with Normal Forms

Author(s) -

Dodson M. M.,

Rynne B. P.,

Vickers J. A. G.

Publication year - 1994

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/49.3.614

Subject(s) - hausdorff dimension , mathematics , urysohn and completely hausdorff spaces , hausdorff distance , effective dimension , hausdorff measure , minkowski–bouligand dimension , diffeomorphism , pure mathematics , dimension (graph theory) , diophantine approximation , inductive dimension , diophantine equation , mathematical analysis , point (geometry) , type (biology) , packing dimension , fractal dimension , geometry , fractal , ecology , biology

The Hausdorff dimension is obtained for exceptional sets associated with linearising a complex analytic diffeomorphism near a fixed point, and for related exceptional sets associated with obtaining a normal form of an analytic vector field near a singular point. The exceptional sets consist of eigenvalues which do not satisfy a certain Diophantine condition and are ‘close’ to resonance. They are related to ‘lim‐sup’ sets of a general type arising in the theory of metric Diophantine approximation and for which a lower bound for the Hausdorff dimension has been obtained.

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