Uniform distribution preserving mappings and variational problems

This paper studies two aspects of uniform-distribution preserving functions. We give a general criterion under which a function of this type can be expected to preserve discrepancy and apply it to study linear mappings and their effect on the isotropic discrepancy. Also, we investigate certain types of variational problems for these functions and establish some connections to uniformly distributed sequences which will then allow us to solve similar variational problems for uniformly distributed sequences by means of these functions and their properties.