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Perturbation of distributionally chaotic operators

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

This paper investigates the dynamics of linear operators which preserve distributional chaos under certain perturbations. A spectral description of the set of linear operators on a Hilbert space which preserve distributional chaos under a small linearly dependent perturbation is obtained. Moreover, several existence results of common distributionally irregular manifolds (absolutely mean irregular manifolds) for the scalar multiples of a linear operator are proved.

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Acknowledgements

The authors would like to thank the referees whose careful reading and suggestions produced an improvement in the presentation of the article.

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, People’s Republic of China

    Zongbin Yin, Zhijing Chen & Yuming Chen

  2. School of Sciences, Southwest Petroleum University, Chengdu, 610500, People’s Republic of China

    Xinxing Wu

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  1. Zongbin Yin
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  2. Zhijing Chen
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  3. Yuming Chen
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  4. Xinxing Wu
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Correspondence to Zongbin Yin.

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This work was supported by the National Natural Science Foundation of China (Nos. 11601449, 11701584, 11701104, 11801096) and Natural Science Research Project of Guangdong Province (No. 2017KQNCX122).

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Yin, Z., Chen, Z., Chen, Y. et al. Perturbation of distributionally chaotic operators. RACSAM 115, 84 (2021). https://doi.org/10.1007/s13398-021-01024-4

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  • DOI: https://doi.org/10.1007/s13398-021-01024-4

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