We prove a necessary and sufficient condition of the topological equivalence of smooth functions with finitely many local extrema defined on a circle.
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V. I. Arnold, “Calculus of snakes and the combinatorial analysis of the Bernoulli, Euler, and Springer numbers of the Coxeter groups,” Usp. Mat. Nauk, 47, Issue 1 (283), 3–45 (1992).
V. I. Arnold, “Bernoulli-Euler updown numbers, associated with function singularities, their combinatorics and arithmetics,” Duke Math. J., 63, No. 2, 537–555 (1991).
L. I. Nicolaescu, Morse Function Statistics, Preprint arXiv: math. GT/0604437 vI 20 Apr 2006 (2006).
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 829–836, June, 2008.
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Yurchuk, I.A. Combinatorial aspects of the topological classification of functions on a circle. Ukr Math J 60, 967–976 (2008). https://doi.org/10.1007/s11253-008-0102-z
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DOI: https://doi.org/10.1007/s11253-008-0102-z