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On the attractors of Feigenbaum maps

Tom 110 / 2014

Guifeng Huang, Lidong Wang Annales Polonici Mathematici 110 (2014), 55-62 MSC: Primary 37B25; Secondary 54H20. DOI: 10.4064/ap110-1-5

Streszczenie

A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every $s\in (0,1)$, we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is $s$.

Autorzy

  • Guifeng HuangDepartment of Basic Science
    Dalian Naval Academy
    116018 Dalian, Liaoning, China
    e-mail
  • Lidong WangDepartment of Mathematics
    Dalian Nationalities University
    116600 Dalian, Liaoning, China
    e-mail

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