Contact unimodal map germs from the plane to the plane

Abstract

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]. 2020 Mathematics Subject Classification. 58Q05, 14H20. Funding. The research of the first author is supported by Higher Education Commission, Pakistan by the Project Number 7495/Punjab/NRPU/R&D/HEC/2017. Manuscript received 21st July 2020, accepted 8th September 2020.