A note on badly approximable linear forms

Bulletin of the Australian Mathematical Society

Volumn 83, Issue 2, 2011, Pages 262-266

  Hussain, Mumtaz ^a  

^a LA TROBE UNIVERSITY   (Australia)

Author keywords

Diophantine approximation; Hausdorff dimension; systems of linear forms

Indexed keywords

EID: 79955059826     PISSN: 00049727     EISSN: 17551633     Source Type: Journal    
DOI: 10.1017/S0004972710002005     Document Type: Article

References (9)

1. H. Dickinson, 'The Hausdorff dimension of the systems of the simultaneously small linear forms', Mathematika 40 (1993), 367-374.
2. D. Dickinson, T. Gramchev and M. Yoshino, 'Perturbations of vector fields on tori: resonant normal forms and diophantine phenomena', Proc. Edinb. Math. Soc. 45 (2002), 731-759.
3. L. Dirichlet, 'Verallgemeinerung eines Satzes aus der Lehre von den Kettenbrüchen nebst einigen Anwendungen auf die Theorie der Zahlen', S.-B. Preuss. Akad. Wiss. (1842), 93-95.
4. M. M. Dodson and J. A. G. Vickers, 'Exceptional sets in Kolmogorov-Arnol'd-Moser theory', J. Phys. A 19 (1986), 349-374.
5. K. J. Falconer, Fractal Geometry-Mathematical Foundations and Applications (Wiley, New York, 1990).
6. M. Hussain and J. Levesley, 'The metrical theory of simultaneously small linear forms', Preprint, arXiv:0910.3428.
7. V. Jarník, 'Über die simultanen Diophantischen Approximationen', Math. Z. 33 (1931), 505-543.
8. A. Khintchine, 'Einige Sätzeüber Kettenbrüche, mit Anwendungen auf die Theorie der Diophantischen Approximationen', Math. Ann. 92 (1924), 115-125.
9. W. M. Schmidt, 'Badly approximable systems of linear forms', J. Number Theory 1 (1969), 139-154.