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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.
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
54H20 Topological dynamics (MSC2010)