Draft:Arnold invariants
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The three Arnold invariants, J+, J- and St, introduced by Vladimir Arnold in 1994, are mathematical entities used to classify closed plane curves. The J+ invariant is defined for closed differentiable curves immersed in the plane. It is a numerical value associated with direct tangencies. The J- invariant is associated with inverse tangencies. The St invariant is related to the number of triple points a curve has.[1][2][3][4]
Sources
- V. I. Arnold, Topological Invariants of Plane Curves and Caustics. University lecture series, Vol. 5, AMS Providence, 1994.
- V. I. Arnold, Plane Curves, Their Invariants, Perestroikas and Classificacions. Advances in Soviet Mathematics, Vol. 21, 1994. American Mathematical Society, 1994.
References
- ^ C. Mendes de Jesus and M.C. Romero Fuster: "Bridges, channels and Arnold’s invariants for generic plane curves", Topology and its Applications 125 (2002) pp. 505–524.
- ^ Sarah Gulde, "Classification of Plane Curves"
- ^ Gusein-Zade, S.M., Natanzon, S.M. (1997). The Arf—invariant and the Arnold invariants of plane curves. In: Arnold, V.I., Gelfand, I.M., Retakh, V.S., Smirnov, M. (eds) The Arnold-Gelfand Mathematical Seminars. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4122-5_13
- ^ Hanna Haeussler: Generalization of Arnold's J+ invariant for pairs of immersions