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Distributionally n-chaotic dynamics for linear operators

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Abstract

This paper investigates distributionally n-chaotic dynamics of linear operators on Fréchet spaces. It is shown that an uncountable distributionally scrambled sets under a linear operator may not be distributionally n-scrambled for any \(n \ge 3\). In addition, the existence of invariant distributionally n-scrambled linear manifolds for a composition operator and for a bilateral weighted shift operator are proved by explicit construction.

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Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their careful reading of the manuscript and their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics, South China University of Technology, Guangzhou, 510640, People’s Republic of China

    Zongbin Yin & Qigui Yang

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  1. Zongbin Yin
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  2. Qigui Yang
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Correspondence to Qigui Yang.

Additional information

This work was partly supported by the National Natural Science Foundation of China (No. 11671149) and the Natural Science Foundation of Guangdong Province (No. 2014A030313256).

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Yin, Z., Yang, Q. Distributionally n-chaotic dynamics for linear operators. Rev Mat Complut 31, 111–129 (2018). https://doi.org/10.1007/s13163-017-0226-5

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  • DOI: https://doi.org/10.1007/s13163-017-0226-5

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