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Distributional chaos on complex sectors. (Chinese. English summary) Zbl 1399.37024
Summary: We characterize the densely distributional chaos for the translation semigroup, with a sector in the complex plane as index set, defined on a weighted function space. A sufficient condition is given for the translation semigroup to be distributionally chaotic in terms of the integrability of the admissible weight function, and in terms of the upper density of a subset of the index set. In addition, we study the index set and show that the translation semigroup is also distributionally chaotic on some subsets of the index set.
MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
54H20 Topological dynamics (MSC2010)
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