Georgia Institute of Technology College of Sciences

The existence of several objects in dynamics can be reduced to the existence of solutions of several functional equations, which then, are dealt with using fixed point theorems (e.g. the contraction mapping principle). This opens the possibility to take numerical approximations and validate them. This requires to take into account truncation, roundoff and other sources of error. I will try to present the principles involved as well as some practical implementations of a basic library. Much of this is work with others including D. Rana, R. Calleja, J. L. Figueras.