6533b7cefe1ef96bd1257af5

RESEARCH PRODUCT

Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets

Robert Roussarie

subject

PhysicsTranscritical bifurcationMathematical analysisSaddle-node bifurcationBogdanov–Takens bifurcationInfinite-period bifurcationSingular point of a curveParameter spaceBifurcation diagramBifurcation

description

In the study of the Bogdanov-Takens unfolding, we introduced in 4.3.5.2 the following formulas of rescaling in the phase-space and in the parameter space: $$ x = {r^2}\bar x,y = {r^3}\bar y,\mu = - {r^4},\nu = {r^2}\bar \nu . $$

https://doi.org/10.1007/978-3-0348-0718-0_6