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- W2976973119 abstract "Let X be a compact Hausdorff space, with uniformity U, and let f:X→X be a continuous function. For D∈U, a D-pseudo-orbit is a sequence (xi) for which (f(xi),xi+1)∈D for all indices i. In this paper we show that pseudo-orbits trap ω-limit sets in a neighbourhood of prescribed accuracy after a uniform time period. A consequence of this is a generalisation of a result of Pilyugin et alia: every system has the second weak shadowing property. By way of further applications we give a characterisation of minimal systems in terms of pseudo-orbits and show that every minimal system exhibits the strong orbital shadowing property." @default.
- W2976973119 created "2019-10-03" @default.
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- W2976973119 date "2019-12-01" @default.
- W2976973119 modified "2023-09-24" @default.
- W2976973119 title "Orbital shadowing, ω-limit sets and minimality" @default.
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- W2976973119 doi "https://doi.org/10.1016/j.topol.2019.106903" @default.
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