Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms

Volume 68 / 1995

Sarah Holte Colloquium Mathematicum 68 (1995), 291-296 DOI: 10.4064/cm-68-2-291-296

Abstract

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 $F:ℝ^2 → ℝ^2$ so that F restricted to its full attracting set, $⋂_{k ≥ 0} F^k(ℝ^2)$, is topologically conjugate to $\widehat f:(I,f) → (I,f)$. In this situation, we say that the inverse limit space, (I,f), can be embedded as the full attracting set of F.

Authors

  • Sarah Holte

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