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TOPOLOGICAL COMPLEXITY OF SEMIGROUP ACTIONS
2008
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.
Keywords:
- Topological degeneracy
- Topological complexity
- Semigroup
- Topological dynamics
- Topological ring
- Topology
- Topological entropy in physics
- Discrete mathematics
- Symmetry protected topological order
- Topological tensor product
- Mathematics
- Bounded function
- Topological algebra
- Topological vector space
- Equicontinuity
- Cover (topology)
- Correction
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