Let \( {\mathbf{F}}:M \times \mathbb{R} \to M \) be a continuous flow on a manifold M, let V ⊂ M be an open subset, and let \( \xi :V \to \mathbb{R} \) be a continuous function. We say that ξ is a period function if F(x, ξ(x)) = x for all x ∈ V. Recently, for any open connected subset V ⊂ M; the author has described the structure of the set P(V) of all period functions on V. Assume that F is topologically conjugate to some \( {\mathcal{C}^1} \)-flow. It is shown in this paper that, in this case, the period functions of F satisfy some additional conditions that, generally speaking, are not satisfied for general continuous flows.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 954–967, July, 2010.
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Maksymenko, S.I. Period functions for \( {\mathcal{C}^0} \)- and \( {\mathcal{C}^1} \)-flows. Ukr Math J 62, 1109–1125 (2010). https://doi.org/10.1007/s11253-010-0417-4
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DOI: https://doi.org/10.1007/s11253-010-0417-4