Exceptional sets for self-affine fractals

Kenneth John Falconer; J. Miao

doi:10.1017/S0305004108001576

Exceptional sets for self-affine fractals

Kenneth John Falconer, J. Miao

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Under certain conditions the 'singular value function' formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension.

Original language	English
Pages (from-to)	669-684
Number of pages	16
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	145
Issue number	3
DOIs	https://doi.org/10.1017/S0305004108001576
Publication status	Published - Nov 2008

Keywords

HAUSDORFF DIMENSION
PROJECTIONS

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10.1017/S0305004108001576

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title = "Exceptional sets for self-affine fractals",

abstract = "Under certain conditions the 'singular value function' formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension.",

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author = "Falconer, \{Kenneth John\} and J. Miao",

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AB - Under certain conditions the 'singular value function' formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of exceptional parameters is small both in the sense of Hausdorff dimension and Fourier dimension.

KW - HAUSDORFF DIMENSION

KW - PROJECTIONS

UR - https://www.scopus.com/pages/publications/54949105396

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DO - 10.1017/S0305004108001576

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EP - 684

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

Exceptional sets for self-affine fractals

Abstract

Keywords

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