On a property specific to the tent map |
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| Authors: | Akihiko Kitada Yoshihito Ogasawara |
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| Affiliation: | Department of Materials Science and Engineering, Laboratory of Mathematical Design for Materials, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan |
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| 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. |
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