Redundant variables: iterated maps and the 2-d Ising model

The period doubling route to chaos in iterated maps has a beautiful renormalization group description first extensively studied by Feigenbaum. The fixed point of the renormalization group can be moved by making a coordinate change, leading to a redundancy in the description. We examine the existence and effect of redundant variables in the renormalization group description of such maps. We relate our analysis to redundant variables in the 2-d Ising model, and conjecture that it may explain some scaling features of the exact solution.