# The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors

Acta Arithmetica (1992)

- Volume: 61, Issue: 1, page 69-81
- ISSN: 0065-1036

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topBryan P. Rynne. "The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors." Acta Arithmetica 61.1 (1992): 69-81. <http://eudml.org/doc/206452>.

@article{BryanP1992,

author = {Bryan P. Rynne},

journal = {Acta Arithmetica},

keywords = {diophantine approximation by restricted sequences of integer vectors; Hausdorff dimension},

language = {eng},

number = {1},

pages = {69-81},

title = {The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors},

url = {http://eudml.org/doc/206452},

volume = {61},

year = {1992},

}

TY - JOUR

AU - Bryan P. Rynne

TI - The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors

JO - Acta Arithmetica

PY - 1992

VL - 61

IS - 1

SP - 69

EP - 81

LA - eng

KW - diophantine approximation by restricted sequences of integer vectors; Hausdorff dimension

UR - http://eudml.org/doc/206452

ER -

## References

top- [1] A. Baker and W. M. Schmidt, Diophantine approximation and Hausdorff dimension, Proc. London Math. Soc. 21 (1970), 1-11. Zbl0206.05801
- [2] R. C. Baker, Singular n-tuples and Hausdorff dimension, Math. Proc. Cambridge Philos. Soc. 81 (1977), 377-385. Zbl0351.10041
- [3] A. S. Besicovitch, Sets of fractional dimensions (IV): On rational approximation to real numbers, J. London Math. Soc. 9 (1934), 126-131. Zbl0009.05301
- [4] I. Borosh and A. S. Fraenkel, A generalization of Jarník's theorem on Diophantine approximations, Indag. Math. 34 (1972), 193-201. Zbl0242.10014
- [5] J. D. Bovey and M. M. Dodson, The Hausdorff dimension of systems of linear forms, Acta Arith. 45 (1986), 337-358. Zbl0534.10025
- [6] M. M. Dodson and J. A. G. Vickers, Exceptional sets in Kolmogorov-Arnol'd-Moser theory, J. Phys. A 19 (1986), 349-374. Zbl0605.34041
- [7] H. G. Eggleston, Sets of fractional dimensions which occur in some problems of number theory, Proc. London Math. Soc. 54 (1951), 42-93. Zbl0045.16603
- [8] V. Jarník, Diophantische Approximationen und Hausdorffsches Mass, Mat. Sb. 36 (1929), 371-382. Zbl55.0719.01
- [9] V. Jarník, Über die simultanen diophantischen Approximationen, Math. Z. 33 (1931), 505-543. Zbl57.1370.01
- [10] V. G. Sprindžuk, Metric Theory of Diophantine Approximations (translated by R. A. Silverman), John Wiley, 1979. Zbl0287.10043

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