Abstract
Topological dynamical systems (X, T) are actions \(T\,{ \times }\, X \rightarrow X\), given as \((t, x) \mapsto tx\), on a compact Hausdorff topological space X with T an acting group or monoid. We consider the property of topological transitivity especially for semiflows (X, S) and discuss variations in its definitions. We emphasize on those properties of transitivity that differ for semiflows as compared to those for flows or (semi)cascades.
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Nagar, A. Revisiting variations in topological transitivity. European Journal of Mathematics 8, 369–387 (2022). https://doi.org/10.1007/s40879-021-00509-1
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DOI: https://doi.org/10.1007/s40879-021-00509-1
Keywords
- Minimality
- Topological transitivity
- Strong transitivity
- Very strong transitivity
- Locally eventually onto
- Strong product transitivity
- Semiflows