Classification of one-state-variable bifurcation problems up to codimension seven
- 1 January 1986
- journal article
- research article
- Published by Taylor & Francis in Dynamics and Stability of Systems
- Vol. 1 (1) , 1-41
- https://doi.org/10.1080/02681118608806002
Abstract
We present a classification of one-state-variable singularities with distinguished parameter through codimension seven. This extends results previously known up to codimension four on contact equivalence with distinguished parameter. Among other interesting phenomena we present the topology of a modal family in codimension five. The classification uses elementary techniques including the notions of tangent space, restricted tangent space, and intrinsic ideals. For each problem of codimension seven or less, a normal form, criteria for recognizing the singularity and a set of unfolding vectors are given. Subordination relations between the different singularities are also described.Keywords
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