QUASICONTINUITY, NONATTRACTING POINTS, DISTRIBUTIVE CHAOS AND RESISTANCE TO DISRUPTIONS

QUASICONTINUITY, NONATTRACTING POINTS, DISTRIBUTIVE CHAOS AND RESISTANCE TO DISRUPTIONS

We prove that any continuous function can be locally approximated at a fixed point $x_{0}$ by an uncountable family resistant to disruptions by the family of continuous functions for which $x_{0}$ is a fixed point. In that context, we also consider the property of quasicontinuity.

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2023-02, Vol.107 (1), p.102-111
Hauptverfasser: KUCHARSKA, MELANIA, PAWLAK, RYSZARD J.
Format: Artikel
Sprache:eng
Schlagworte:
Continuity (mathematics)
Dynamical systems
Fixed points (mathematics)
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Zusammenfassung:We prove that any continuous function can be locally approximated at a fixed point $x_{0}$ by an uncountable family resistant to disruptions by the family of continuous functions for which $x_{0}$ is a fixed point. In that context, we also consider the property of quasicontinuity.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972722001101