Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms
Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 291-296
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_cm_68_2_291_296,
author = {Sarah Holte},
title = {Embedding inverse limits of nearly {Markov} interval maps as attracting sets of planar diffeomorphisms},
journal = {Colloquium Mathematicum},
pages = {291--296},
publisher = {mathdoc},
volume = {68},
number = {2},
year = {1995},
doi = {10.4064/cm-68-2-291-296},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-68-2-291-296/}
}
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Sarah Holte. Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms. Colloquium Mathematicum, Tome 68 (1995) no. 2, pp. 291-296. doi: 10.4064/cm-68-2-291-296
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