4 papers
A quantitative Khintchine-Groshev type theorem over a field of formal series
M. M. Dodson, S. Kristensen, J. Levesley
An asymptotic formula which holds almost everywhere is obtained for the number of solutions to the Diophantine inequalities |qA-p|<ψ(|q|), where A is an n by m matrix (m>1) over th…
Zero-infinity laws in Diophantine approximation
Y. Bugeaud, M. M. Dodson, S. Kristensen
It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does…
Hausdorff Dimension and Diophantine Approximation
M. Maurice Dodson, Simon Kristensen
We begin with a brief treatment of Hausdorff measure and Hausdorff dimension. We then explain some of the principal results in Diophantine approximation and the Hausdorff dimension…
Exceptional sets in dynamical systems and Diophantine approximation
M M Dodson
The nature and origin of exceptional sets associated with the rotation number of circle maps, Kolmogorov-Arnol'd-Moser theory on the existence of invariant tori and the linearisati…