Randomized trial identifies orbit maps in definable C^r groups, suggesting implications for group actions.
Let M=(R,+,・,<,...) be an o-minimal expansion of the standard structure R=(R,+,・,<) of the field of real numbers. Let G be a definable C^r group and H a definable C^r subgroup of G. We prove that if M. admits the C^ω (resp. C^∞) cell decomposition or 0 ≤ r < ∞, then the orbit map π : G → G
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Tomohiro KAWAKAMI (2008) studied this question.
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