Draft:Arnold invariants

Submission declined on 28 October 2024 by Ldm1954 (talk).

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Declined by Ldm1954 56 days ago. Last edited by Ldm1954 56 days ago. Reviewer: Inform author.

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Comment: There is essentially the same material already in Vladimir Arnold. You have to make it more informative for it to be relevant. Ldm1954 (talk) 01:55, 28 October 2024 (UTC)

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

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[1] 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.

[2] Sarah Gulde, "Classification of Plane Curves"

[3] 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

[4] Hanna Haeussler: Generalization of Arnold's J+ invariant for pairs of immersions

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