On -genericity of distributional chaos
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Abstract Let M be a compact smooth manifold without boundary. Based on results by Good and Meddaugh [Invent. Math.220 (2020), 715–736], we prove that a strong distributional chaos is $C^0$ -generic in the space of continuous self-maps (respectively, homeomorphisms) of M. The results contain answers to questions by Li, Li and Tu [Chaos26 (2016), 093103] and Moothathu [Topology Appl.158 (2011), 2232–2239] in the zero-dimensional case. A related counter-example on the chain components under shadowing is also given.
2018 ◽
pp. 96-102
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2011 ◽
Vol 57
(2)
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pp. 409-416
2019 ◽
Vol 50
(1)
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pp. 129-155
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2010 ◽
Vol 7
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pp. 90-97
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2019 ◽
Vol 35
(5)
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pp. e3187
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