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On a property specific to the tent map

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  • Kitada, Akihiko
  • Ogasawara, Yoshihito

Abstract

Let a set {Xλ;λ∈Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace Xλ to define a map gXλ:Xλ→X which has the following property specific to the tent map known in the baker’s transformation. Namely, for any infinite sequence ω0,ω1,ω2,… of Xλ, λ∈Λ, we can find an initial point x0∈ω0 such that gω0(x0)∈ω1,gω1(gω0(x0))∈ω2,…. The conditions are successfully applied to a closed cover of a weak self-similar set.

Suggested Citation

  • Kitada, Akihiko & Ogasawara, Yoshihito, 2006. "On a property specific to the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1256-1258.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:5:p:1256-1258
    DOI: 10.1016/j.chaos.2005.08.159
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    References listed on IDEAS

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    1. Kitada, Akihiko & Ogasawara, Yoshihito, 2005. "On a decomposition space of a weak self-similar set," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 785-787.
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    Cited by:

    1. Kitada, Akihiko & Ogasawara, Yoshihito & Eda, Katsuya, 2008. "Note on a property specific to the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 104-105.

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    1. Kitada, Akihiko & Ogasawara, Yoshihito & Eda, Katsuya, 2008. "Note on a property specific to the tent map," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 104-105.
    2. Kitada, Akihiko & Ogasawara, Yoshihito & Yamamoto, Tomoyuki, 2007. "On a dendrite generated by a zero-dimensional weak self-similar set," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1732-1735.

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