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QUASICONTINUITY, NONATTRACTING POINTS, DISTRIBUTIVE CHAOS AND RESISTANCE TO DISRUPTIONS

Part of: Maps and general types of spaces defined by maps Real functions Topological dynamics

Published online by Cambridge University Press:  06 October 2022

MELANIA KUCHARSKA Open the ORCID record for MELANIA KUCHARSKA [Opens in a new window]  and
RYSZARD J. PAWLAK Open the ORCID record for RYSZARD J. PAWLAK [Opens in a new window]
MELANIA KUCHARSKA
Affiliation:
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland e-mail: melania.kucharska@edu.uni.lodz.pl
RYSZARD J. PAWLAK*
Affiliation:
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland
*
e-mail: ryszard.pawlak@wmii.uni.lodz.pl
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Abstract

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.

Keywords

quasicontinuitydistributive chaosDC1 pointnonattracting pointresistance to disruptions

MSC classification

Primary: 26A18: Iteration
Secondary: 37B40: Topological entropy 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) 54C70: Entropy
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 1 , February 2023 , pp. 102 - 111
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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