This thesis is concerned with rigorous computation of dynamical quantities. In particular, we provide rigorous computation of diffusion coefficients for uniformly expanding maps of the interval. Moreover, we provide a rigorous computational scheme for linear response and we apply it in the case of uniformly expanding circle maps. Our results have been implemented successfully on a computer. Examples are included to illustrate the computer implementation.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.