The Topological Sensitivity with respect to Furstenberg Families
In this work, a dynamical system X,f means that X is a topological space and f:X⟶X is a continuous map. The aim of the article is to introduce the conceptions of topological sensitivity with respect to Furstenberg families, n-topological sensitivity, and multisensitivity and present some of their ba...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/7684072 |
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| Summary: | In this work, a dynamical system X,f means that X is a topological space and f:X⟶X is a continuous map. The aim of the article is to introduce the conceptions of topological sensitivity with respect to Furstenberg families, n-topological sensitivity, and multisensitivity and present some of their basic features and sufficient conditions for a dynamical system to possess some sensitivities. Actually, it is proved that every topologically ergodic but nonminimal system is syndetically sensitive and a weakly mixing system is n-thickly topologically sensitive and multisensitive under the assumption that X admits some separability. |
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| ISSN: | 1026-0226 1607-887X |