Geodesic
On Prime Immersions of S 1 into R 2
Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 589-593

Voir la notice de l'article provenant de la source Cambridge University Press

A C 1-mapping ƒ from the oriented circle S1 into the oriented plane R2 such that f f’ (t) ≠ 0 for all t is called a regular immersion. We call a point p in Im f a double point if f-1(p) is a two element set with the corresponding tangent vectors being linearly independent. A regular immersion which is one-to-one except at a finite number of points whose images are double points is called a normal immersion. The work of Whitney [7], Titus [3] and Verhey [6] shows that the normal immersions form a dense open subset in the space of regular immersions with the usual C 1-topology, and can be characterized up to diffeomorphic equivalence by a combinatorial invariant called the intersection sequence. 
Martin, John R. On Prime Immersions of S 1 into R 2. Canadian journal of mathematics, Tome 28 (1976) no. 3, pp. 589-593. doi: 10.4153/CJM-1976-057-5
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