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The construction of global attractors. (English) Zbl 0714.58036
Let f: \(I\to I\) be a continuous interval mapping and let J denote the inverse limit of the system \[ ...\to^{f}I\to^{f}I\to^{f}I \] with g: \(J\to J\) the map induced by f. It is shown that (J,g) can be topologically realized as a global attractor in the plane.
Reviewer: M.Mrozek

MSC:
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
54H20 Topological dynamics (MSC2010)
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[1] Marcy Barge and Joe Martin, Chaos, periodicity, and snakelike continua, Trans. Amer. Math. Soc. 289 (1985), no. 1, 355 – 365. · Zbl 0559.58014
[2] Marcy Barge and Joe Martin, Dense orbits on the interval, Michigan Math. J. 34 (1987), no. 1, 3 – 11. · Zbl 0655.58023
[3] Marcy Barge and Joe Martin, Dense periodicity on the interval, Proc. Amer. Math. Soc. 94 (1985), no. 4, 731 – 735. · Zbl 0567.54024
[4] R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653 – 663. · Zbl 0043.16804
[5] Morton Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478 – 483. · Zbl 0113.37705
[6] William Thomas Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math. 103 (1982), no. 2, 589 – 601. · Zbl 0451.54027
[7] R. F. Williams, One-dimensional non-wandering sets, Topology 6 (1967), 473 – 487. · Zbl 0159.53702
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