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A note on expansive $\mathbb{Z}^k$-action and generators
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We define the concept of a generator for a $\mathbb{Z}^k$-action $T$ and show that $T$ is expansive if and only it has a generator. Further, we prove several properties of a $\mathbb{Z}^k$-action including that the least upper bound of the set of expansive constants is not an expansive constant.
Abstract
We define the concept of a generator for a $\mathbb{Z}^k$-action $T$ and show that $T$ is expansive if and only it has a generator. Further, we prove several properties of a $\mathbb{Z}^k$-action including that the least upper bound of the set of expansive constants is not an expansive constant.
참고문헌 (10)
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- 김대정, "SPECTRAL DECOMPOSITION OF k-TYPE NONWANDERING SETS FOR Z2-ACTIONS", 대한수학회보, 51(2), pp.387~400 (2014), 대한수학회
- C. Mouron, "Continua that admit expansive Zn+1 actions but not expansive Zn actions", Houston J. Math, 36(1), pp.167~180 (2010)
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- Sergei Yu. Pilyugin, "Shadowing in actions of some Abelian groups", Fundamenta Mathematicae, 179(1), pp.83~96 (2003), Institute of Mathematics, Polish Academy of Sciences[DOI]
- Raphael M. Robinson, "Undecidability and nonperiodicity for tilings of the plane", Inventiones Mathematicae, 12(3), pp.177~209 (1971), Springer Science and Business Media LLC[DOI]
- En Hui Shi, "The Nonexistence of Expansive ℤ d Actions on Graphs", Acta Mathematica Sinica, English Series, 21(6), pp.1509~1514 (2005), Springer Science and Business Media LLC[DOI]
- Enhui Shi, "A nonexistence of expansive Zn actions on Peano continua that contain no θ-curves", Topology and its Applications, 154(2), pp.462~468 (2007), Elsevier BV[DOI]
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