Sensitivity for topologically double ergodic dynamical systems
| Autor: | Xiaofang Yang, Yongxi Jiang, Tianxiu Lu, Bridge Non-destruction Detecting, Risong Li |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
ergodic (resp. strongly ergodic) multi-sensitivity Mathematics::Dynamical Systems Dynamical systems theory General Mathematics 010102 general mathematics Space (mathematics) sensitivity 01 natural sciences 010305 fluids & plasmas Surjective function Combinatorics Metric space Compact space Integer 0103 physical sciences QA1-939 Ergodic theory Inverse limit 0101 mathematics multi-sensitivity syndetic sensitivity Mathematics |
| Zdroj: | AIMS Mathematics, Vol 6, Iss 10, Pp 10495-10505 (2021) |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2021609?viewType=HTML |
| Popis: | As a stronger form of multi-sensitivity, the notion of ergodic multi-sensitivity (resp. strongly ergodically multi-sensitivity) is introduced. In particularly, it is proved that every topologically double ergodic continuous selfmap (resp. topologically double strongly ergodic selfmap) on a compact metric space is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive). And for any given integer $ m\geq 2 $, $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ f^{m} $. Also, it is shown that if $ f $ is a continuous surjection, then $ f $ is ergodically multi-sensitive (resp. strongly ergodically multi-sensitive) if and only if so is $ \sigma_{f} $, where $ \sigma_{f} $ is the shift selfmap on the inverse limit space $ \lim\limits_{\leftarrow}(X, f) $. Moreover, it is proved that if $ f:X\rightarrow X $ (resp. $ g:Y\rightarrow Y $) is a map on a nontrivial metric space $ (X, d) $ (resp. $ (Y, d') $), and $ \pi $ is a semiopen factor map between $ (X, f) $ and $ (Y, g) $, then the ergodic multi-sensitivity (resp. the strongly ergodic multi-sensitivity) of $ g $ implies the same property of $ f $. |
| Databáze: | OpenAIRE |
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