Domokos, Gábor and Holmes, Philip and Lángi, Zsolt (2015) A genealogy of convex solids via local and global bifurcations of gradient vector fields. Journal of Nonlinear Science. ISSN 09388974 (Submitted)

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Abstract
Threedimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies these are nondegenerate maxima, minima, and saddlepoints, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work it was shown that these classifications are complete in that no class is empty. Here we construct 1 and 2parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddlenode and saddlesaddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g. by abrasion of sedimentary particles.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria 
Depositing User:  Dr. Zsolt Lángi 
Date Deposited:  11 Sep 2015 11:29 
Last Modified:  11 Sep 2015 11:29 
URI:  http://real.mtak.hu/id/eprint/26390 
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