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Topological complexity of semigroup actions
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In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.
Abstract
In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.
참고문헌 (5)
- S. Ferenczi, "Measure-theoretic complexity of ergodic systems", Israel Journal of Mathematics, 100, pp.189~207 (1997)
- S. Ferenczi, "Complexity of sequences and dynamical systems", Discrete Mathematics, 206(1), pp.145~154 (1999)
- F. Blanchard, "Topological complexity", Ergodic Theory and Dynamical Systems, 20(3), pp.641~662 (2000)
- K. E. Petersen, "Disjointness and weak mixing of minimal sets", Proc. Amer. Math. Soc., 통권 : 24, pp.278~280 (1970)
- J. de Vries, "Elements of topological dynamics, Mathematics and its Applications", pp.257~ (1993), Kluwer Academic Publishers Group
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