Draft:Arnold invariants

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

Thank you for your submission, but the subject of this article already exists in Wikipedia. You can find it and improve it at Arnold invariants instead.

If you would like to continue working on the submission, click on the "Edit" tab at the top of the window.
If you have not resolved the issues listed above, your draft will be declined again and potentially deleted.
If you need extra help, please ask us a question at the AfC Help Desk or get live help from experienced editors.
Please do not remove reviewer comments or this notice until the submission is accepted.

Where to get help

If you need help editing or submitting your draft, please ask us a question at the AfC Help Desk or get live help from experienced editors. These venues are only for help with editing and the submission process, not to get reviews.
If you need feedback on your draft, or if the review is taking a lot of time, you can try asking for help on the talk page of a relevant WikiProject. Some WikiProjects are more active than others so a speedy reply is not guaranteed.

How to improve a draft

Wikipedia:Contributing to Wikipedia – a basic overview on how to edit Wikipedia.
Help:Wikitext – how to use the markup
Help:Referencing for beginners – how to include references
Wikipedia:Article development – how to develop your article
Wikipedia:Writing better articles – how to improve your article
Wikipedia:Verifiability – make sure your article includes reliable third-party sources

You can also browse Wikipedia:Featured articles and Wikipedia:Good articles to find examples of Wikipedia's best writing on topics similar to your proposed article.

Improving your odds of a speedy review

To improve your odds of a faster review, tag your draft with relevant WikiProject tags using the button below. This will let reviewers know a new draft has been submitted in their area of interest. For instance, if you wrote about a female astronomer, you would want to add the Biography, Astronomy, and Women scientists tags.

Add tags to your draft

Editor resources

Easy tools: Citation bot (help) | Advanced: Fix bare URLs

Declined by Ldm1954 21 days ago. Last edited by Ldm1954 21 days ago. Reviewer: Inform author.

Resubmit

Please note that if the issues are not fixed, the draft will be declined again.

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

This article is a stub. You can help Wikipedia by expanding it.

[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

[1]

[2]

[3]

[4]