A Remark on Invariant Scrambled Sets

Lin Huang; Huo Yun Wang; Hong Ying Wu

doi:10.4028/www.scientific.net/AMM.204-208.4776

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 204-208A Remark on Invariant Scrambled Sets

A Remark on Invariant Scrambled Sets

Abstract:

By a dynamical system we mean a compact metric space together with a continuous map . This article is devoted to study of invariant scrambled sets. A dynamical system is a periodically adsorbing system if there exists a fixed point and a periodic point such that and are dense in . We show that every topological weakly mixing and periodically adsorbing system contains an invariant and dense Mycielski scrambled set for some , where has no isolated points. A subset is a Myceilski set if it is a countable union of Cantor sets.