### Abstract

Let a set {X_{λ}; λ ∈ Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace X_{λ} to define a map g_{Xλ} : X_{λ} → X which has the following property specific to the tent map known in the baker's transformation. Namely, for any infinite sequence ω_{0}, ω_{1}, ω_{2}, ... of X_{λ}, λ ∈ Λ, we can find an initial point x_{0} ∈ ω_{0} such that {Mathematical expression}. The conditions are successfully applied to a closed cover of a weak self-similar set.

Original language | English |
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Pages (from-to) | 1256-1258 |

Number of pages | 3 |

Journal | Chaos, Solitons and Fractals |

Volume | 29 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2006 Sep |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

*Chaos, Solitons and Fractals*,

*29*(5), 1256-1258. https://doi.org/10.1016/j.chaos.2005.08.159

**On a property specific to the tent map.** / Kitada, Akihiko; Ogasawara, Yoshihito.

Research output: Contribution to journal › Article

*Chaos, Solitons and Fractals*, vol. 29, no. 5, pp. 1256-1258. https://doi.org/10.1016/j.chaos.2005.08.159

}

TY - JOUR

T1 - On a property specific to the tent map

AU - Kitada, Akihiko

AU - Ogasawara, Yoshihito

PY - 2006/9

Y1 - 2006/9

N2 - 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 {Mathematical expression}. The conditions are successfully applied to a closed cover of a weak self-similar set.

AB - 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 {Mathematical expression}. The conditions are successfully applied to a closed cover of a weak self-similar set.

UR - http://www.scopus.com/inward/record.url?scp=33645867373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645867373&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2005.08.159

DO - 10.1016/j.chaos.2005.08.159

M3 - Article

AN - SCOPUS:33645867373

VL - 29

SP - 1256

EP - 1258

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 5

ER -