A note on the IPF algorithm when the marginal problem is unsolvable

In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2 x 2 x 2 contingency table whose pair marginals are all equal to a specified 2 x 2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a "period three limit cycle" attracting all positive initial tables, and a-bifurcation occur when the parameter crosses the threshold.