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Self-generation of self-replicating maps of an interval
Published online by Cambridge University Press: 19 September 2008
Abstract
We construct C1 symmetric maps of [−1, 1] to itself, satisfying a condition similar to Feigenbaum's: -φ(x) = φ(-x), φ2(bx) = bφ(x), 0<b <1. Under certain conditions, the non-wandering set consists of the one-sided Morse minimal set together with 2n points of period 2n for each n = 1, 2, … The main significance of the construction is its simplicity. Given a certain piece of the map φ, the rest is generated by the required equation.
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