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

• Autorzy: Bryan P. Rynne
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1992
• Tom: 61
• Numer: 1
• Strony: 69-81

Daty

wydano

1992

otrzymano

1990-12-12

Twórcy

autor

Bryan P. Rynne

• Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland

Bibliografia

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