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Topologically conjugate function
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[QUOTE="pasmith, post: 4836122, member: 415692"] You need [itex]h(x^2) = 2h(x)[/itex] for all [itex]x \in \mathbb{R}[/itex]. The left hand side is an even function, so [itex]h[/itex] must itself be even. We can ensure that by taking [itex]h(x) = p(|x|)[/itex] for some [itex]p : \{x \in \mathbb{R} : x > 0\} \to \mathbb{R}[/itex]. Do you know of any functions defined on [itex]x > 0[/itex] with the property that [itex]p(x^\alpha) = \alpha p(x)[/itex]? [/QUOTE]
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Topologically conjugate function
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