Mathematical Proceedings of the Cambridge Philosophical Society



Simultaneous Diophantine approximation on the circle and Hausdorff dimension


H. DICKINSON a1 and M. M. DODSON a1
a1 Department of Mathematics, University of York, York YO10 5DD.

Abstract

The functional relations between the coordinates of points on a manifold make the study of Diophantine approximation on manifolds much harder than the classical theory in which the variables are independent. Nevertheless there has been considerable progress in the metric theory of Diophantine approximation on smooth manifolds. To describe this, some notation and terminology are needed.

(Received September 21 1999)
(Revised February 2 2000)