Hausdorff dimension and a generalized form of simultaneous Diophantine approximation

• Autorzy: B. P. Rynne , H. Dickinson
• Języki publikacji: EN

Kategorie tematyczne

• 11J83: Metric theory
• 28A78: Hausdorff and packing measures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 1
• Strony: 21-36

Daty

wydano

2000

poprawiono

1999-10-11

otrzymano

1999-12-22

Twórcy

autor

B. P. Rynne

• Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, U.K.

autor

H. Dickinson

• Department of Mathematics, University of York, York YO1 5DD, U.K.

Bibliografia

• [1] A. S. Besicovitch, Sets of fractional dimension (IV): On rational approximation to real numbers, J. London Math. Soc. 9 (1934), 126-131.
• [2] I. Borosh and A. S. Fraenkel, A generalization of Jarník's theorem on Diophantine approximations, Indag. Math. 34 (1972), 193-201.
• [3] J. D. Bovey and M. M. Dodson, The Hausdorff dimension of systems of linear forms, Acta Arith. 45 (1986), 337-358.
• [4] M. M. Dodson, Hausdorff dimension, lower order and Khintchine's theorem in metric Diophantine approximation, J. Reine Angew. Math. 432 (1992), 69-76.
• [5] M. M. Dodson and J. A. G. Vickers, Exceptional sets in Kolmogorov-Arnol'd-Moser theory, J. Phys. A 19 (1986), 349-374.
• [6] . R. Dombrovski, Simultaneous approximations of real numbers by algebraic numbers of bounded degree, Dokl. Akad. Nauk BSSR 33 (1989), 205-208.
• [7] H. G. Eggleston, Sets of fractional dimension which occur in some problems in number theory, Proc. London Math. Soc. 54 (1952), 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), 503-543.
• [10] B. P. Rynne, The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors, Acta Arith. 61 (1992), 69-81.
• [11] B. P. Rynne, Hausdorff dimension and generalized Diophantine approximation, Bull. London Math. Soc. 30 (1998), 365-376.
• [12] V. G. Sprindžuk, Metric Theory of Diophantine Approximations (translated by R. A. Silverman), Winston, Washington, 1979.