Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/21341
Title: A Classifier for Map Germs of Modality ≤ 1
Authors: Aslam, Saima
Keywords: Physical Sciences
Mathematics
Issue Date: 2022
Publisher: Government College University, Faisalabad
Abstract: The aim of this thesis is to study, develop and implement certain algorithms in order to find the type of map germs with modality 1. We present a characterization of the different types of map germs in terms of certain invariants and use this characterization to identify the type of map germs without computing the normal form. We describe our implementation in the computer algebra system SINGULAR. Therefore, we discuss four problems in this thesis. In first problem, we characterize the classification of all map germs from the plane to the plane of the Boardman symbols (2; 1) given by Dimca and Gibson with respect to K-equivalence by means of easy computable invariants such as the codimension of tangent space, the Milnor number of the given map, the double fold number and a number which is closely connected with the order of k-determinacy. In the second problem, we correct the classification of unimodal map germs from plane to the plane of the Boardman symbol (2; 2) given by Dimca and Gibson with respect to K-equivalence. Also, we characterize this classification by means of easy computable invariants. In the third problem, we characterize the classification of equidimensional contact unimodal map germs from (C3; 0) ! (C3; 0) given by Dimca and Gibson in terms of invariants . In the fourth problem, we characterize the classification of unimodal maps from the plane to the plane with respect to the A-equivalence given by Rieger in terms of invariants such as the codimension of tangent space, the Milnor number of the critical set of the given map germ, the double fold number and the multiplicity of a map germ. iii
Gov't Doc #: 26805
URI: http://prr.hec.gov.pk/jspui/handle/123456789/21341
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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