Abstract
A universal family of differentiable functions on S1 in the sense of Jänich [3], Def. 6, is explicitely given by means of trigonometric polynomials. We also give a geometric description of the universal family of order 4, which is closely related to Zeemans catastrophe machine.
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Bröcker, T. Universelle Familien differenzierbarer Funktionen auf der Kreislinie. Manuscripta Math 48, 275–290 (1984). https://doi.org/10.1007/BF01169011
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DOI: https://doi.org/10.1007/BF01169011