The Recognition of the Bifurcation Problem with Trivial Solutions

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.