Hausdorff dimension of chaotic attractors in a class of nonsmooth systems

Denghui Li, Pengcheng Miao* (Corresponding Author), Jianhua Xie, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Fractal dimension is a important feature of a chaotic attractors. Generally, the rigorous value of Hausdorff dimension of a chaotic attractor is not easy to compute. In this work, we consider a class of nonsmooth systems. Initially, we determine a set of parameter values in which the systems have a chaotic attractor with an Sinai-Ruelle-Bowen measure. Then we give a lower bound and an upper bound of the Hausdorff dimension of the attractor. Our rigorous analysis shows that the two bounds are equal, and thus the exact formula of the Hausdorff dimension of the attractor is obtained. Moreover, the relationship between the Hausdorff dimension and the parameter values is discussed in terms of the derived formula.
Original languageEnglish
Article number111218
Number of pages7
JournalChaos, Solitons and Fractals
Volume151
Early online date17 Jul 2021
DOIs
Publication statusE-pub ahead of print - 17 Jul 2021

Keywords

  • chaotic attractor
  • Hausdorff dimension
  • SRB measure

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