On the finiteness of attractors for piecewise maps of the interval
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We consider piecewise $C^{2}$ non-flat maps of the interval and show that, for Lebesgue almost every point, its omega-limit set is either a periodic orbit, a cycle of intervals or the closure of the orbits of a subset of the critical points. In particular, every piecewise $C^{2}$ non-flat map of the interval displays only a finite number of non-periodic attractors.
2003 ◽
Vol 131
(11)
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pp. 3547-3551
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1994 ◽
Vol 447
(1930)
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pp. 413-437
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2019 ◽
Vol 40
(9)
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pp. 2571-2592
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1997 ◽
Vol 17
(6)
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pp. 1267-1287
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1996 ◽
Vol 08
(08)
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pp. 1161-1185
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2000 ◽
Vol 20
(5)
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pp. 1391-1403
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1995 ◽
Vol 05
(05)
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pp. 1339-1349
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