Extremal manifolds and hausdorff dimension

Duke Mathematical Journal

Volumn 101, Issue 2, 2000, Pages 271-281

  Dickinson, H ^a   Dodson, M ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134846     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-00-10126-3     Document Type: Article

References (21)

1. A. Baker, Transcendental Number Theory, Cambridge Univ. Press, London, 1975.
2. A. Baker and W. M. Schmidt, Diophantine approximation and Hausdorff dimension, Proc. London Math. Soc. (3) 21 (1970), 1-11.
3. R. C. Baker, Dirichlet's theorem on Diophantine approximation, Math. Proc. Cambridge Philos. Soc. 83 (1978), 37-59.
4. V. Beresnevich and V. Bernik, On a metrical theorem of W. Schmidt, Acta Arith. 75 (1996), 219-233.
5. V. I. Bernik, Application of the Hausdorff dimension in the theory of Diophantine approximations (in Russian), Acta Arith. 42 (1983), 219-253.
6. V. I. Bernik, A proof of Baker 's conjecture in the metric theory of transcendental numbers (in Russian), Dokl. Akad. NaukSSSR 277 (1984), 1036-1039.
7. M. M. Dodson, B. P. Rynne, and J. A. G. Vickers, Metric Diophantine approximation and Hausdorff dimension on manifolds, Math. Proc. Cambridge Philos. Soc. 105 (1989), 547-558.
8. M. M. Dodson, B. P. Rynne, and J. A. G. Vickers, Diophantine approximation and a lower bound for Hausdorff dimension, Mathematika 37 (1990), 59-73.
9. M. M. Dodson, B. P. Rynne, and J. A. G. Vickers, Khintchine-type theorems on manifolds, Acta Arith. 57 (1991), 115-130.
10. K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Math. 85, Cambridge Univ. Press, Cambridge, 1986.
11. D. Y. Kleinbock and G. A. Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds, Ann. of Math. (2) 148 (1998), 339-360.
12. J. F. Koksma, Diophantische Approximationen, Springer-Verlag, Berlin, 1974.
13. J. Kubilius, On an application of I. M. Vinogradov's method to the solution of a problem of the metrical theory of numbers (in Russian), Dokl. Akad. Nauk SSSR 67 (1949), 783-786.
14. P. Mattila, Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge Stud. Adv. Math. 44, Cambridge Univ. Press, Cambridge, 1995.
15. B. P. Rynne, Regular and ubiquitous systems, and -dense sequences, Mathematika 39 (1992), 234-243.
16. W. M. Schmidt, Metrische Sätze über simultane Approximation abhängiger Grössen, Monatsh. Math. 68 (1964), 154-166.
17. V. G. Sprindzuk, Mahler's Problem in Metric Number Theory, Transl. Math. Monogr. 25, Amer. Math. Soc., Providence, 1969.
18. V. G. Sprindzuk, Metric Theory of Diophantine Approximations, Scripta Ser. Math., Wiley, New York, 1979.
19. V. G. Sprindzuk, Achievements and problems of the theory of Diophantine approximations (in Russian), Uspekhi Mat. Nauk 35 (1980), 3-68, 248
20. V. G. Sprindzuk, Achievements and problems of the theory of Diophantine approximations (in Russian), Math. Surveys 35 (1980), 1-80.
21. A. I. Vinogradov and G. V. Chudnovsky, “The proof of extremality of certain manifolds” in Contributions to the Theory of Transcendental Numbers, Math. Surveys Monogr. 19, Amer. Math. Soc., Providence, 1984, 421-447.