True Zero Eigenvalues Catastrophe Points

For a function where most points yeE are non-stationary, there are the stationary points which organize the global qualitative topography. Briefly said, you get most information by looking at the points with striking mathematical behaviour  

True zero eigenvalues of the Hessian occur if the potential energy, E, 

We discuss the simplest two cases, namely a potential which is cubic in one (i) or in two (ii) degrees of freedom. 

A peculiarity occurs if the parameter varies from negative values 

On the other hand, the catastrophe point y 0 of the term y is easy 

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