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## Colloquium Mathematicum

1995 | 68 | 2 | 291-296
Tytuł artykułu

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

Autorzy
Treść / Zawartość
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EN
Abstrakty
EN
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.
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Czasopismo
Rocznik
Tom
Numer
Strony
291-296
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-07-16
poprawiono
1994-08-08
Twórcy
autor
• Department of Mathematics, University of Missouri-Rolla, Rolla, Missouri 65401, U.S.A.
Bibliografia
• [Ba] M. Barge, A method for construction of attractors, Ergodic Theory Dynamical Systems 8 (1988), 331-349.
• [BB] M. Barge and M. Brown, Problems in dynamics on continua, in: Continuum Theory and Dynamical Systems, M. Brown (ed.), Amer. Math. Soc., Providence, R.I., 1991, 177-182.
• [BK] M. Barge and J. Kennedy, Continuum theory and topological dynamics, in: Open Problems in Topology, J. van Mill and G. M. Reed (eds.), North-Holland, Amsterdam, 1990, 633-644.
• [BM] M. Barge and J. Martin, The construction of global attractors, Proc. Amer. Math. Soc. 110 (1990), 523-525.
• [Bl] L. Block, Diffeomorphisms obtained from endomorphisms, Trans. Amer. Math. Soc. 214, 403-413.
• [H] S. Holte, Generalized horseshoe maps and inverse limits, Pacific J. Math. 156 (1992), 297-305.
• [M] M. Misiurewicz, Embedding inverse limits of interval maps as attractors, Fund. Math. 125 (1985), 23-40.
• [Sc] R. Schori, Chaos: An introduction to some topological aspects, in: Continuum Theory and Dynamical Systems, M. Brown (ed.), Amer. Math. Soc., Providence, R.I., 1991, 149-161.
• [Sz] W. Szczechla, Inverse limits of certain interval mappings as attractors in two dimensions, Fund. Math. 133 (1989), 1-23.
• [W] R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473-487.
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