Advanced Search

In this paper we address the following question due to Marcy Barge: For what f:I → I is it the case that the inverse limit of I with single bonding map f can be embedded in the plane so that the shift homeomorphism $\widehat{f}$ extends to a diffeomorphism ([BB, Problem 1.5], [BK, Problem 3])? This question could also be phrased as follows: Given a map f:I → I, find a diffeomorphism $F:{ℝ}^2\to {ℝ}^2$ so that F restricted to its full attracting set, ${\bigcap }_{k\ge 0}{F}^k\left({ℝ}^2\right)$, is topologically conjugate to $\widehat{f}:(I,f)\to (I,f)$. In this situation, we say that the inverse...