Ukrainian Mathematical Journal

, Volume 60, Issue 6, pp 967–976 | Cite as

Combinatorial aspects of the topological classification of functions on a circle

  • I. A. Yurchuk

We prove a necessary and sufficient condition of the topological equivalence of smooth functions with finitely many local extrema defined on a circle.


Local Minimum Global Minimum Global Maximum Local Extremum Coxeter Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    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).Google Scholar
  2. 2.
    V. I. Arnold, “Bernoulli-Euler updown numbers, associated with function singularities, their combinatorics and arithmetics,” Duke Math. J., 63, No. 2, 537–555 (1991).zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    L. I. Nicolaescu, Morse Function Statistics, Preprint arXiv: math. GT/0604437 vI 20 Apr 2006 (2006).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • I. A. Yurchuk
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyivUkraine

Personalised recommendations