Abstract
This paper studies the recognition criterion of the bifurcation problem with trivial solution. The t-equivalence is different from the strong equivalence studied by Golubitsky et al. The difference is that the second component of the differential homeomorphism is not identical. Consider the normal subgroup of t-equivalence group, we obtain the characterization of higher order terms P ( h ) . In addition, we also explore the properties of intrinsic submodules and the finite determinacy of the bifurcation problem.
Highlights
Singularity theory offers an extremely useful approach to bifurcation problems
We explore the properties of intrinsic submodules and the finite determinacy of the bifurcation problem
Many authors have studied the classifications of bifurcation problems up to some codimension in a given context by singularity theory
Summary
Many authors have studied the classifications of bifurcation problems up to some codimension in a given context by singularity theory. These classifications include the following three components:. We are interested in knowing precisely when a bifurcation problem is equivalent to a given normal form This problem can often be reduced to the finite dimensions problem by the idea from singularity theory that is finite determinacy. In Reference [6], Vutha and Golubitsky applied singularity theory and adaptive dynamics theory to study evolutionarily stable strategies and convergence stable strategy of strategy functions, they gave the classification with a codimension up to 3 under the action of strategy equivalent group and the solutions to the recognition problems of these normal forms. Assume that the function germs in this paper are smooth
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