Several transitive properties and Devaney’s chaos

Wang, Tao; Yin, Jian Dong; Yan, Qi

doi:10.1007/s10114-016-5050-1

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Chris Good and Sergio Macías1

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2018

2024

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Cited by 2 publications

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“…Wang et al [39] state that non-metric spaces do not admit a notion of sensitivity. In [38], Wang et al consider various versions of Devaney chaos in the light of various notions related to transitivity.…”

Section: Chris Good and Sergio Macíasmentioning

confidence: 99%

What is topological about topological dynamics?

Good¹,

Macı́as²

2018

Discrete &Amp; Continuous Dynamical Systems - A

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We consider various notions from the theory of dynamical systems from a topological point of view. Many of these notions can be sensibly defined either in terms of (finite) open covers or uniformities. These Hausdorff or uniform versions coincide in compact Hausdorff spaces and are equivalent to the standard definition stated in terms of a metric in compact metric spaces. We show for example that in a Tychonoff space, transitivity and dense periodic points imply (uniform) sensitivity to initial conditions. We generalise Bryant's result that a compact Hausdorff space admitting a c-expansive homeomorphism in the obvious uniform sense is metrizable. We study versions of shadowing, generalising a number of well-known results to the topological setting, and internal chain transitivity, showing for example that ω-limit sets are (uniform) internally chain transitive and weak incompressibility is equivalent to (uniform) internal chain transitivity in compact spaces.

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Section: Chris Good and Sergio Macíasmentioning

confidence: 99%