The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
The Hausdorff dimension of self-affine fractals
Abstract
If T is a linear transformation on ℝ n with singular values α 1 ≥ α 2 ≥ … ≥ α n, the singular value function ø s is defined by where m is the smallest integer greater than or equal to s. Let T 1, …, T k be contractive linear transformations on ℝ n. Let where the sum is over all finite sequences (i 1, …, i r) with 1 ≤ i j ≤ k. Then for almost all (a 1, …, a k) ∈ ℝ nk, the unique non-empty compact set F satisfying has Hausdorff dimension min{d, n}. Moreover the ‘box counting’ dimension of F is almost surely equal to this number.
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Cites
Furstenberg, H., & Kesten, H. (1960) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177705909 · Cited by 1,047
Furstenberg, H. (1963) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1963-0163345-0 · Cited by 984
Hausdorff dimension, orthogonal projections and intersections with planes
Mattila, P. (1975) · Annales Academiae Scientiarum Fennicae Series A I Mathematica · doi:10.5186/aasfm.1975.0110 · Cited by 177
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Buehler, M. J. (2024) · ACS Engineering Au · doi:10.1021/acsengineeringau.3c00058 · Cited by 82
Metadata
- Authors
- Falconer, K. J.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1988-03
- Volume
- 103
- Issue
- 2
- Pages
- 339-350
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2111963011
- Cited by
- 353
- References
- 3
- FWCI
- 3.54
- Type
- journal article
- Language
- en
- Open access
- closed
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- Falconer, K. J. (1988). The Hausdorff dimension of self-affine fractals. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100064926
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