Contact unimodal map germs from the plane to the plane

Muhammad Ahsan Binyamin; Saima Aslam; Khawar Mehmood

doi:10.5802/crmath.114

Théorie des singularités

Contact unimodal map germs from the plane to the plane

Muhammad Ahsan Binyamin ¹ ; Saima Aslam ¹ ; Khawar Mehmood ²

¹ Department of Mathematics, GC University, Faisalabad, Pakistan
² Department of Applied Mathematics & Statistics, Institute of Space Technology P.O.Box 2750, Islamabad 44000, Pakistan

Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 923-930.

Résumé

In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol $(2, 2)$ given by Dimca and Gibson. Also, we characterize this classification of unimodal map germs in terms of certain invariants. Moreover, on the basis of this characterization we present an algorithm to compute the type of unimodal map germs of the Boardman symbol $(2, 2)$ without computing the normal form and give its implementation in the computer algebra system Singular [8].

Reçu le : 2020-07-21
Accepté le : 2020-09-08
Publié le : 2020-12-03

DOI : 10.5802/crmath.114

Classification : 58Q05, 14H20

Affiliations des auteurs :

Muhammad Ahsan Binyamin ¹ ; Saima Aslam ¹ ; Khawar Mehmood ²

¹ Department of Mathematics, GC University, Faisalabad, Pakistan
² Department of Applied Mathematics & Statistics, Institute of Space Technology P.O.Box 2750, Islamabad 44000, Pakistan

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Muhammad Ahsan Binyamin and Saima Aslam and Khawar Mehmood},
     title = {Contact unimodal map germs from the plane to the plane},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {923--930},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
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     year = {2020},
     doi = {10.5802/crmath.114},
     language = {en},
}

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Muhammad Ahsan Binyamin; Saima Aslam; Khawar Mehmood. Contact unimodal map germs from the plane to the plane. Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 923-930. doi : 10.5802/crmath.114. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.114/

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