# zbMATH — the first resource for mathematics

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)
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.