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On a property specific to the tent map

Akihiko Kitada and Yoshihito Ogasawara

Chaos, Solitons & Fractals, 2006, vol. 29, issue 5, 1256-1258

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:29:y:2006:i:5:p:1256-1258

DOI: 10.1016/j.chaos.2005.08.159

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