Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms
Holte, Sarah
Colloquium Mathematicae, Tome 68 (1995), p. 291-296 / Harvested from The Polish Digital Mathematics Library
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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 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:ℝ2→ℝ2 so that F restricted to its full attracting set, ⋂k≥0Fk(ℝ2), is topologically conjugate to 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.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:210313 
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     author = {Sarah Holte},
     title = {Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms},
     journal = {Colloquium Mathematicae},
     volume = {68},
     year = {1995},
     pages = {291-296},
     zbl = {0827.54027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv68i2p291bwm}
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Holte, Sarah. Embedding inverse limits of nearly Markov interval maps as attracting sets of planar diffeomorphisms. Colloquium Mathematicae, Tome 68 (1995) pp. 291-296. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv68i2p291bwm/

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